The Rubicon will benefit from a t-case drop after installing a 3"+ suspension lift the same as any TJ does. The only difference with the Rubicon is its transfer case output shaft does not have a slip-joint. Instead, the Rubicon's slip-joint is on its conventional non-CV driveshaft instead of on the t-case output shaft like a non-Rubicon TJ.
The spinning nut is a somewhat common problem. You can fix it by chiseling the bottom of the nut-flange off the frame and then inserting a weld-in nut like you can buy from McMaster-Carr, an online supplier of hardware. Check out McMaster-Carr
Adjustable length control arms won't help since you are still running the stock conventional driveshaft. The pinion angle is critical and trying to adjust it to get rid of vibes with the OE conventional driveshaft is either impossible or nearly impossible.
The best solution is to replace your conventional driveshaft with a CV driveshaft like Tom Wood makes. That will then require adjustable length upper control arms so you can adjust the pinion angle upward to match the CV driveshaft's requirements.
Or get the t-case lowering kit installed but you might also need a set of 1" taller motor mounts since a 1" t-case lowering kit is often not enough to cure the vibes caused by 3"+ suspension lifts. The cost of the combined t-case lowering kit and 1" taller motor mounts is less than a CV driveshaft and adjustable-length control arms but the latter solution is the right way to go.