Just to report back in case anyone else has a similar question in the future:

I did leave Khasab at about 6:15 AM and ended up pulling into DXB T3 around 9:30. Better early than late! And the EK lounge was a fine place to sit for several hours.

The signage to get into the parking lot where the rental car return is located was not the greatest, and I ended up doing a loop around the whole thing after missing the turn I was supposed to take. Once I did get inside the garage, there is no signage at all as to where the various rental agency return offices are, but I just asked one of the garage staff and got pointed in the right direction.

I was returning to Avis at 9:30 AM on a Sunday and it took about five minutes to process.