Reliability of steering and front drive train components is what you will read about the most, that of course is directly affected by style of driving and amount of offroading. There are some mods and aftermarket replacements for the most often failed parts.
I have an H3 Alpha with about 42,000. Only thing so far was a leaking front seal.
My Alpha, loaded up and outfitted with winch, brush guard, UCP, Rock rails and such and weighs in about 6001 lbs before I eat!
I tow either my work trailer loaded down at about 3500 lbs or my Whaler which is about the same. Even with the Alpha with an Auto it really likes 3rd gear. I have tried running overdrive and it will depending on terrain. Last trip it got as good or slightly better mpg running in 3rd.
However that is with a Flashpaq in tow mode. With the load you are considering that would be something to look into since it has options you can program to your needs, not a fixed setting.
I have considered adding brakes to both my trailers. It's ok most of the time, it's those surprise hard braking situations I wish for more! I run 315 tires so that affects braking as well. I often shift down rather than standing on the brake.
These are older pictures of my 06 I-5. I traded partly because of the equipment I have bolted on and stuff I carry and towing, when the 08 Alpha came out I grabbed one.

 

Hunner, I can't believe how "stock" your 2006 looks in this picture!

 

It was several hours new at that time and I tried towing everything I had to see how it did.
It was "Like a Virgin!"
In 2006 there was not much aftermarket "stuff" to buy either. It came with those "nifty" chrome side steps. Took me 2 years to sell those.
Things change, Huh?

 

Two random questions:
1) does it have a low oil light or just a low oil pressure light?
2) does it have a low coolant level light or just overheat light?

In both cases I ask because the girlfriend may drive it from time to time... and she's not the best at checking such things.

 

And... one last question (and then I'm done, I swear!).

I'd like to test sit in one. One of my wants from the H3T is a functional 4 seater car. My DD is a 2 door 4 seat coupe-- not the greatest for driving 4 people around. Further, I'm 6'4.

So, I'd really like to find an H3T that I could sit in and then see how much space there is behind me.

Side note: All hope is not lost for the back seat-- I sit much more forward than most people who are 6'4.

Any suggestions on how to go about that? I've only ever seen one H3T in the wild, and never any at any dealers...

 

I'm six foot and the backseat is okay for adults if I move the driver's seat forward... otherwise, kids only. The H3T doesn't seem to have as much backseat room as an H3... that is what I used to drive.

 

Couple thoughts. If you really can't find one at a dealership, you might find a local T owner on this board willing to meet up and let you look it over. If that doesn't work, you can get an idea by just looking at specs and compare them to other vehicles that you can go sit in, own, etc. Not perfect, but better than nothing. Unless you plan to buy one sight unseen or buy the first one you come across, you are going to have to start looking at them in person anyway.

 

I also went from a 3 to a T and while I've never ridden in the back it did seem a bit different. I just looked it up on Edmunds, the 3 has almost 2 inches more legroom, but the T has ~4" more hip room.

 

That's bad news, 2 inches is significant and I really need this to be a functional 4 seater!

I'd love to just test sit on in a dealer, but there's just none around. Honestly, I've only seen one H3T in real life, ever!

 

Good to know my fat *** and short legs are a custom fit for the backseat of a "T."