The NV3550 usually makes a rumbling noise when sitting in neutral with the clutch out. Sounds like gears rattling and rolling over. It's nothing to be worried about—just the input shaft spinning the bearings, and it's loud because the TJ has no sound-proofing. It usually gets louder the longer the TJ has been running and the hotter the transmission gear oil is. (Adding Red Line MTL usually helps quiet it).
As for the slipping—that's obviously worrisome. Hopefully it's just the boot as your mechanic says. It should be up to them to get this right.
As for the slipping—that's obviously worrisome. Hopefully it's just the boot as your mechanic says. It should be up to them to get this right.