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ChanW said: PP

Interesting summary @WilliamA! Thank you. So, does "resetting the computer" by disconnecting the battery, cause it to relearn from the beginning, or does it retain its 'blocks'? Would that help it to learn the 'trailer towing' block more quickly?

Also, with my manual transmission, does higher RPM (for example climbing a hill while towing) cause more (or less) overall stress or wear, as long as the temperature gauge is normal?

My theory has always been that 4500RPM is fine, for example if the red line is at 5200.

It's been some time since I did any troubleshooting of this detail so my opinion may be a bit dated by rapid advances but the theory is pretty much unchanged.  That said, when you disconnect the battery, it should do a couple of things: first, it will erase the stored trouble codes.  Second, it should reset most parameters to "factory" preset values.  That provides a valuable tool for technicians (switched from "mechanics" for now obvious reasons) to see if the trouble code immediately repeats, pointing to the suspect fault. It gets muddy here because some codes are triggered by component failure and sometimes by parameter.  For example, the dreaded O2 sensor my be a mechanical problem with the sensor itself.  Other times, the sensor may be mechanically sound but reading a condition in the exhaust that is out of bounds from what the computer expects to see as a minimum or maximum.  Often, the condition causing sensor failure failure will in time destroy the sensor, leading to not one but two problems: out of range condition AND sensor failure!  In that case, replacing the sensor without troubleshooting and mitigating the cause will just lead to another sensor failure.  The technicians' bane is that these things can quickly escalate into stupifyingly complex problems with multiple root causes.  This is often made worse because neither the shop nor customer wants to pay for seemingly unrelated diagnostic time leading to vehicles going out the door with no codes, but the original gremlin still happily in residence under the hood.  Seemingly unrelated issues raise havoc with everything and ultimate causes may appear (if they appear at all!) only by thorough examination of.....well.....everything.  Overheating may turn out to be a transmission issue.  O2 sensor failure may ultimately be caused by the fuel pump or pressure regulator. 
As a side note, it's my humble opinion that the worst thing you can do as a user is to try and eliminate your own problem by wiping the memory, ie, disconnecting the battery.  This seldom (never?) fixes the problem and erases the computers' record of parameters leading up to the failure.  It's the same action as having the maid clean the room at a crime scene, THEN calling in the investigator.  The computer memory overwrites itself in an endless loop, but there will certainly be valuable information stored so long as its not erased before diagnosis occurs.  The technician will certainly erase the memory, but he'll download the history first.  Things seldom happen in a vacuum (sic) and GM, or Ford, or whoever, engineers will want that fault file.  If you erase it, it's almost guaranteed that the first thing you've accomplished is added diagnostic time onto your bill.  As a driveability technician, the thing I dreaded most to hear from my mech-savvy customers was: "she threw a code, so I erased it to see if it would come back".  Grrrrrrrrr....Ka-ching!  Technician makes a mental note to add 3 hours to the estimate....
In industry parlance, these are called "driveability" problems.  That's the guy in the shop with the computer workstation in his bay with the Deerhunter cap and pipe, sifting data in an effort to root out the head gremlin.  These guys are often found reading manuals at night and on days off, monitoring the internet for trends and tips. They work hard because the system demands it.  It's difficult, challenging, occasionally rewarding and constantly changing.  I've been that guy and am still bothered 15 years later by "the one that got away".
Speaking to the point of the thread as I suspect I should, the plugged catalytic converter problem is a widely known issue and speaking only for myself, I'd have looked there early in the diagnostic chain.  Many factors weigh on overlooking the obvious and any tech worth his/her weight in axle grease would publicly commiserate and privately wipe brow and thank the grand technician that "it wasn't me".  Faults happen and good people have bad days.  I can site examples of great techs missing simple things, like a friend who replaced 5 transfer cases in Bronco II's under a Ford recall and not putting oil in ANY of them.  This stuff happens.  Patience and understanding may be difficult commodities to distribute, particularly if you're the one writing the check.  But I promise you one thing: technicians sweat blood over this kind of thing, every day... And 15 years later, we lay awake thinking about them.

So.... Shifting and RPM's:  I don't (won't) give advice on that save to tell you how I do it.  My T@G trailer and Jeep Wrangler go down the road....any road...dirt, goat trail, superslab, like I would drive a horse pulling a buggy.  I let "Ole Hurricane" have her reins and determine how hard to run.  If you pay attention to the car, it will tell you where it's comfortable.  The term "redline" refers to the point within an engine beyond which parts will begin to exit their environs (quickly) and have nothing whatever to do with efficiency.  I try to remember that if the engine is screaming, so is everything behind it.  If Hurricane wants to downshift 2 gears and loaf up the hill, I let her.  She'll tell me where she's comfortable.  That's (mostly) what the right lane is for.

FAST.
RELIABLE.
CHEAP.
pick any two...
WilliamA 

Interesting summary @WilliamA! Thank you. So, does "resetting the computer" by disconnecting the battery, cause it to relearn from the beginning, or does it retain its 'blocks'? Would that help it to learn the 'trailer towing' block more quickly?

Also, with my manual transmission, does higher RPM (for example climbing a hill while towing) cause more (or less) overall stress or wear, as long as the temperature gauge is normal?

My theory has always been that 4500RPM is fine, for example if the red line is at 5200.

There are really only 3 basic causes for a plugged catalytic converter:
1. Too much fuel (bad plugs, etc)
2. Burning oil.
3. Coolant leaking into the combustion cycle (head gasket, etc)
let's not forget that it may be a combination of causes but the result will be melting of the ceramic coating within the converter that plugs the metal screen.  The commin thread is excessive heat in the converter.  Very often, the culprit condition may exist but not be bad enough to notice until another factor (like towing a trailer) exacerbates the condition, making it worse.  Modern control systems have gotten much better at mitigating and managing engine management to the point where such problems are not evident until an event (towing) radically alters the computers block learn integrator (yes, that's  a real thing. It's motor-eze for how your cars' computer "learns".)  The computer stores events (also called "start cycles") in blocks, then compares them to develop and average how much fuel, air timing advance etc the engine needs during a typical "start cycle".  The computer meters fuel etc to make the engine as efficient as possible within the given parameters.  Then, you pull a trailer...or dramatically alter the use of the vehicle in a way that falls outside of the specifications of the block learn, which is basically a rolling, constantly updating 2 dimensional array of numbers.  When that happens, the computer is unable to compensate enough and has to make the best choice available to protect the engine.  The computer default is to add fuel and retard timing to reduce overheating in the engine, which conversely causes overheating in the exhaust as there is almost certainly a rich condition caused by too much unburned fuel.  When this happens, it won't necessarily set a trouble code as the engine itself is still within the operating parameters of heat etc.  Given enough time, excessive fuel delivery will set a code but the computer is programmed to "be patient" and wait a number of data cycles before the bells and lights go off.  That's why an event such as this may happen without setting off a warning light.  
As an aside, it's within the realm of possibility for something as unconnected as transmission temperature to cause plugging of the converter.  The transmission sheds its heat through the radiator.  If that causes overheating in the coolant and thus, the engine, the computer will try to cool the engine by richening the fuel mixture and...voila...a plugged converter!  I am not saying that's the cause.  I'm saying that it's a "system" so apparently unrelated problems can appear as gremlins throughout that system.  When the mechanic tries to diagnose the problem,  the actual fault has disappeared altogether leaving only some failed component upstream or downstream as its "victim".  It takes very little time for an overextended system to be outside parameters long enough to plug the converter.  After the fact, it may be difficult or impossible to reproduce the fault.  Then, the mechanic must fall back on his or her own "block learn" (experience) to come up with a diagnosis.  It should also be noted that often, when the owner looks back,  he or she remembers something ignored that "wasn't quite right."
The sad mantra of we mechanics has always been not a matter of "if", but "when" we make the wrong call.
WilliamA 

not sure if this helps, if you have your TV owners manual,  look at the emission warranty.  I think they are extended past the normal vehicle warranty.  Something like 75000 miles or so.  Just an idea to help with the cost.  Safe travels!