I doubt that you have a band problem. The change that takes place from 2nd to 3rd is the engagement of the forward clutch pack. Actually, this is a somewhat common problem with "RE" transmissions. The piston seals wear out at an accelerated rate and cause an RPM flareup from 2nd to 3rd, or no 3rd gear at all. There is an updated forward clutch assembly (from Mopar) available that uses a different style piston and drum.
As this requires removal of the transmission, I'd at least check the other clutch packs and replace the seals while I was in there. Flushing the trans cooler is strongly recommended.
I have no idea about prices. I just work on them; the service writers deal with the money
I'm just putting in my opinion; as I have not actually driven or worked on your Jeep, I couldn't be absolutely sure that the forward clutch is the problem.
Hope I helped