Nice-Looking setup!!
From a handling perspective, good stiff wall tires and the right tongue weight need to be paid close attention. If the new tires you buy are 10 ply side wall, they should work great for towing (vs a passenger rated tire). 6-ply isn't too bad, but the taller tire the more side-to-side wallow might be expected. Experiment with tongue weight to see what the best combo is with your rig ..move gear around in the trailer and box as much as possible to get the right combo. I'm sure you know all these things and have experimented already, but just a reminder.
I personally wouldn't blow money on any of those aftermarket intake/exhaust add-ons or chips. Many feel the intakes don't perform as claimed (per a lot of sites out there) and they probably just accelerate wear on your vehicle. But you would definitely get more acceleration out of chipping it. There's no doubt that a re-gear would change the RPM range you'd be in on the road. There's a lot of snake-oil pitches out there. Different guys are going to give ya different opinions, so take mine with a grain of salt. Maybe just driving more careful and conservatively during towing is the best and cheapest 'secret formula'. Finally, there's always the proven engine-performance mods (cam/heads, etc) you could consider.
Does you H3 have a overdrive lock-out button or towing mode? It's frustrating that in 07 (my year) GM didn't include features which had been common on other premium vehicles for several years back then (mainly Jeeps and P-U's). If your's doesn't have a lock-out button or towing mode, it should be possible to rig up a 5th gear lock-out. That might be the best and least expensive add for towing. You would preserve on-road fuel economy for the 90% of most driving, yet get towing power when you needed it.
You have a long wheelbase so the tail shouldn't wag the dog too bad.