Yeh, the wobble I have is only around 90 so I think it's balance/tyre related rather than any more sinister. Fingers crossed anyway.
I noticed on the photos you posted in the for sale section that your old tyres have load rating of E (10 ply). That might explain why they were giving a firmer ride. Most of the smaller 265/70/17 tyres are usually E rated and a lot of people complain that they are too firm for the relatively light JK (they're originally designed for the heavier F trucks and the likes in the states). I thought all 285/70/17's were D rated (8 ply) though, as mine are, but clearly that is not the case. I've just checked on the Cooper and Mickey T websites and sure enough the 285/70/17 ST Maxx are 10 ply and the 285/70/17 4-Ribs are 8 ply.
Now for the not so good news. I also noticed that MT have the 285/70/17 P3's showing as 10 ply, so the same as your old Coopers. Given that MT and Coopers are basically the same company I'd say it's good bet that they are very similar construction. Might not bode well for your ride quality with the P3's. Be interested to know how you get on with them. It's nice that you've got a year or so to test drive them and see how they feel before my tyres will need changing