Here's some JK "ride" tips.
1) Rubi's come with the "towing package" shock / coil kits by default. (What I'm running and still too soft for my jeeps' weight). Not really going to help by swapping if the ride is harsh.
2) Toyo's are UBER stiff tires, I run my BFG KM2s at 26-28 front/rear MAX. If I've got loads of stuff in the back, like several hundreds lbs worth, I might air the rear up to 30 just to save some gas. I'd try Bill's pressure range. I've seen Toyos on trails at 8 PSI and they still seem like rock hard pucks while mine are all smooshy.
3) Having a slight forward rake or having slightly lower front end pressure helps to put more positive pressure on the front wheels and makes it less "flighty / darty" when driving. Holds a straight line better. I've got a 2 door, so not sure how that'll translate to the longer wheelbase.
That's all I've got from driving my JK so far.