The advice here is going in all directions. If the vehicle is feeling bouncy, then you've overloaded the springs - fixing anything else may mask the problem to an extent, but even if it does it would only be a band aid solution. On a vehicle with progressive rate springs, the ride will get rougher as you load it up to a point - the load will compress the weaker portion of the spring so that the vehicle doesn't have the same 'float' that you're used to. After that point though, you'll then overload the main portion of the spring and the ride will become soft and bouncy. That's where you are. Two ways to fix this - different springs or air bags. If loading the jeep down is an occasional thing, then the air bags may be the way to go, since they won't affect your day to day drive. If you're going to be doing this a lot, however, then definitely look at stiffer springs. The best way to get the right springs, imo, is to load up the jeep and then go get it weighed. Then you can call OME, tell them the load, and they'll fix you up with the right springs for your use.
A lift would exacerbate the problem - any benefit you might get from it would be incidental to the lift itself; i.e., stiffer springs. However, if you move the weight higher you're just making the problem worse. If you want a lift for other reasons, then sure, kill two birds with one stone, but be realistic that the lift is actually working against the load problem.
Stiffer shocks or adjustable shocks might mask the problem but you're only fixing the rate of compression, not the amount. And you'd transfer force to the shocks and mounts that probably hasn't been designed in - probably O.K., but why not fix the problem itself? You may find though that you'd prefer adjustable shocks to go along with the new springs/air bags.
Related to the above, you're also likely feeling some added sway - the rear anti-sway bar on the wrangler is pretty weak. If you can find one (IF), then a stiffer sway bar would help as well.
The problem with fixing load-related problems on a jeep is that you're swimming upstream against what most of the after market is pushing. 98% of the wrangler after market I'm convinced is off-road bling with engineering an afterthought, if it's given any thought at all. That's why I recommend going with OME - they've got a lot of experience that goes beyond just making jeeps taller.