I ran 31s for a long time (close to 10 years) when my Jeep was my DD with nothing more than shackle lift and bastard packs that had a second leaf from some S10 packs added to the stock packs. It rubbed the flares when flexing, but didn't make it to the body. I drive about 70 miles a day and it's very hilly in my area. It wasn't a powerhouse, but it could run 70+ as long as it was relatively flat, 65-70 on hills. I'm running 33s now and it's not that much different, but I have aluminum wheels and Hankook Dynapro MTs. The Hankooks aren't terribly aggressive for a MT tire and they weigh about the same as my old 31s.
Concerning the transmission, sooner or later 5th is going to fall off. The bigger the tire, the more likely that it will happen. The AX5 might make a great boat anchor, but they're terrible transmissions. I just don't use 5th anymore. I'm planning a Ford 302/NP435 swap right now (haven't decided on a TC). If my transmission gives up again, I'll be expediting the swap, but I doubt it will be a factor since I don't use 5th.
The rear axle is a wild card. I know guys who are downright abusive who haven't had problems and I've seen them let go for no apparent reason. I wouldn't worry about it right now, but since you're wheeling, you should probably start thinking about swapping it if you're going to 33s (or even aggressive wheeling on 31s). I've messed up two on 31s. If you decide to wait, do NOT put a locker in your D35. It will self destruct.
For wheeling, bigger tires make things easier, but even with stock tires you'd be amazed where you can put a YJ (it just takes more skill). There's only 1" of clearance more with 33s in lieu of 31s, but 33s have a much easier time going over things (just as 35s climb easier than 33s). Most people think that you put on bigger tires for more clearance; however, while clearance is nice, it's not nearly as much of an issue when wheeling as diameter of tire when you're trying to get over or through something.
The pretty picture below illustrates how the angle of the tangent of the tire to an obstacle changes with tire diameter on a few different sizes of obstacles. The closer the angle gets to 180 (flat) the easier it is to climb. A degree or two makes a world of difference. I hope this clears up what I mean about tire size for climbing rather than clearance.
The bottom line is, the transmission and rear axle that came in your Jeep just suck (I'm in the same boat). They are the weak points in your drive train. Bigger tires exacerbate the problem. Deeper gears would help (not cure) concerns about the transmission, but won't do all that much for the rear end (except throw money away by swapping gears into a D35).
Just decide what tires you want to run and plan accordingly. At the moment, I've got 33s with the same drivetrain that you've got and it's holding up fine. I'm prepping to reinstall my 8.8 now and I'm planning on swapping to a different engine/trans/TC, but my end goal isn't the 33s that I'm running. I want to go bigger. For 33s, I don't see a terrible problem with the setup you have. I wouldn't run 35s with it, but I'm comfortable with my 33s.