The internet is full of such projects, so do some research and learn from the mistakes of others. To clear the bike when turning sharp, and when backing, the hitch assembly will need to be extended beyond normal. This will provide more leverage at the hitch so tongue weight might not be so bad as one might expect, a good thing. A longer tongue will also extend the trailer wheelbase, which takes away a lot of sway. Another good thing. I'd still invest in a
friction sway control if intending to tow with a relatively small vehicle.
Equalizer bars would still level the entire rig if properly installed and adjusted, even with the axle moved rearward, but on smaller vehicles the front axle weight rating and/or tire capacities are sometimes easily exceeded, so calculate carefully. Tow vehicle axle weight and tire weight ratings have put the whoas on several rig combinations people wanted when I worked for a trailer manufacturer. Some things just can't be done safely.
As for air conditioning, get a small, cheap window unit from Walmart ($115), mount it down low on the back wall to help with the hitch load, and a few deep cycle batteries ($100 each off brands with core charges) just in front of the back bumper to run it when no solar or shore is available. Build a small duct to carry the cooled air up the back wall and use the roof to disperse it. Cold air in tiny spaces can be annoying if blowing right on you.
You can build a small but effective generator just for batteries from a lawn engine ($100 new) and a high output car or truck alternator (105 amp Chevy 1-wire with built in regulator, $105 with shipping). I've seen such home made rigs that cost little more than time to collect junk parts from wrecks and such. You can mount a small generator back next to the batteries. More help with the hitch load.
Those big tires will probably carry the extra weight no problem, but you may need a heavier axle and springs. Heavier axle and springs costs less than equalizer bars by about $150, and that pays for your Walmart AC. Of course, you'll pretty much have to build the trailer yourself or have it custom built, and the price difference for a heavier axle and springs is just a few dollars. You can shop around and get a complete axle and springs with hubs for well under $200. If I was going to tow with a small vehicle, I'd look for electric brakes. 2000 pound axle, springs, brakes, hubs--everything under the frame except wheels and tires, can be had for about $350. Just weld it up and mount the wheels.
You will never regret investing in excellent axle, brake, and hitch systems. Sadly, you will regret not making such investments when looking at your rig without good systems upside down in a ditch. The smaller, lighter the tow vehicle, the more critical system quality becomes.
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