I'd be very concerned about the exhaust because of the camper shell creating a semi-closed environment.  Also, wouldn't you have to hop up into the bed to pull the starter rope on the generator?  Do you have enough clearance for your arm on the pull within the shell?

Michele: It is from Northern Tool  and has a few pictures John

Ultra-Tow Hydraulic Hitch Mount Crane — 30in. - 84in. Lift Range, 1,000-Lb. Capacity

Jenn:  The Honda 2000i we have is 45 lbs. The height from the Platform is only about 2' and  Kris & I can lift it alone and I have a back back hip and knee brace. John
You could look and West Marine I believe they have a device that mounts on a railing that they use to pick up and lower outboard motors. We used one several years ago to lower our outboard down to our small tender . I believe you could attach it to one of the outboard arms on the Platform. I would still go to Camping World and try picking one of the 2000i's up first. John

Michele: Go to Camping World and see what lifting 45lbs Honda 2000i is like. They may even bring one out to your TV to try.

Michele Here is  lift I was talking about

Oops - upon closer examination, that may be a photo of two 2000W Yamahas (even though I Googled the 1000 model).  I also can't find any mention of the parallel feature for the 1000s.

I have a flat tonneau cover over my GMC Canyon truck bed and the Honda 2000i fits right under it (with anti-theft handle). I have to open the cover all the way to access where I keep the generator locked (close to the cab).

My truck bed has a thick rubber mat as a bed liner. The generator pulls well (gotta keep a foot on it when pulling the cord though). Even with the tonneau cover all the way folded back (it's a "BackFlip model"), the exhaust still can accumulate low in the bed. I pointed the exhaust to match the wind direction and could still smell it. Echoing or increased noise was not an issue. The genny did not move from where I put it (still locked to the bed too).

There's a wheeled cart you can buy just for the Honda 2000i. It's a cute little thing, but the handle does not fit under my tonneau cover. You can run the generator on the wheeled cart (http://www.amazon.com/gp/product/B00CSBUXJW?psc=1&redirect=true&ref_=oh_aui_detailpage_o08_s00). Still have to lift it into the truck bed though.

Pop-T@B,
Quiet.... Do you know how it compares to the Honda for noise? I've heard the Honda, and it's pretty quiet, so it seems to be something of a standard.

Pop-T@B said:

Boo, I have Westinghouse WH2000iXLT , it is very quiet, very easy to pick up one handed. If you can pick up a 5 gallon water tote, you can pick this generator up. I am very pleased with it, out of the box added the oil and gas, started on the first pull. Has a super long run time on a tank of fuel. 

There was a negative Amazon review stating it would not work above elevations of 7,000 feet:

21 of 25 people found the following review helpful

Seems to be an excellent inverter generator design

By David on June 16, 2015

Verified Purchase

Seems to be an excellent inverter generator design. I did have to re-gap the spark plug before it would start on one or 2 pulls as advertised. The specs called for .032 inch gap and the product came with the spark plug gapped at .028 inches. After re-setting the gap it starts easily. Now, however, I have to try and return it for a refund. Why? Well I purchased this as a source of power to go camping with. I live in the
Denver area and it runs fine here. However, the camping is in the mountains and I just learned the reason it would not start this weekend was that it can't run above 7,000 feet! We were camped at 7,500, and most places we travel with our RV are 8,000 and as high as 9,500. Westpro Systems tells me there is no replacement carburetor jet to fix this mixture issue, and therefore it's of no use to me. It would have been nice if their product information on-line, or the specifications on-line made some note of this altitude issue. If you live or play at altitude, buy something else.

In my travels, it's almost all Honda - Once in awhile a Yamaha - Lots of red everywhere you look.
In my current campground, 100% Honda.

I ordered the Wen yesterday. I've been wanting to have some sort of generator for a long while for hurricane season anyway. Once my electrical issues on the T@B are sussed out I'm sure I'll be testing it to see how/if it handles the little Kenmore A/C.

boo - then it works for ya - nothin wrong with stayin east.

There are lots of places in the west that would work (just not all).  So for instance, while Bryce campground is at 8,000 ft, coda chrome, just down the road would be fine (5,800 elevation).  While you would have to do some planning, if you decided to venture westward, you could find sites that would work with your generator (in Yellowstone, Mammoth and Madison are both below 7,000 sf).  

I'm sure there are some areas, particularly in utah and colorado) that you'd have to plan carefully, but in general most of west has campground areas that are located within the limitations of the generator.   Would just take a little more planning to  make sure there isn't an issue.  Just recognize it's a potential constraint on sites and include this in your planning.