Recommend PSI 33’s 285/70/17 Pro Comp MT2 M/T
 

I have the same rims with Duratrac 33's and run them at 36 on tow different Jeeps - a '07 2dr and an '14 4dr. Seems to be a good number for me including snow and rain. No bounce, no steering shimmy, definitely no death wobble which I had with my last '07 4dr and stock tires on the alloy wheels.

I would drop them down to like 32 to start, then chalk test to find a pressure with a good wear pattern. Probably going to be between 28-32.

Take your wheels off and make sure that those lock rings on the hubs are taken off. Also are the wheels matched to the hub bore?

30 psi would be a good starting point.

I have the exact same tires size 315 x 70 r17. I have them at 40 with zero shaking of any kind up to 90 mph. 4 door with 3" lift. Of course, I was shaking like a mutha too before I had my ball joints, track bar, & steering stabilizer replaced. The addition of brackets for my lower control arms along with new balanced rubber and alignment didn't hurt either.

My guess is, if you have some mileage on your rig and/or installed the lift yourself, the shaking ain't coming from your new tires. Of course, if you're mostly stock with low mileage then yeah... you probably should just start with a rebalance and make sure your alignment is correct. You should get an alignment whenever you get new tires but that goes without saying.