Now that I think about it, if the gauge reads "full" when the tank is not, it's probably reading empty when it's not quite empty either. So when you go to fill up, you're not able to add as much fuel as per usual because the tank isn't really empty.
As you mentioned in your earlier post, you can just replace the sending unit. That involves dropping the tank and removing the pump. So given all that, it may be wise just to replace the complete pump module given that you probably have a lot of miles on your Jeep and it's a fairly big job to do.
A complete pump module comes with the pump, filter assembly, and the sending/level assembly, all integrated together.
PM me if you'd like pricing - I sell genuine Mopar replacement parts to JeepForum members at 25% off what you'd pay at the dealership.