Ohhhhh, yeah on a trailer I think you are alright to go unregistered. Check with the two states though. Your current state to make sure there are no penalties for allowing the reg. to lapse. Then again to the new state to be sure they don't have issues with you bringing in an unregistered vehicle.
As for reimbursement, I'm positive you get reimbursed. I overpaid when I bought my Canyon at the dealership and DMV sent me a check for the difference. And I live in CALIFORNIA! Seriously though-check with your local DMV. Should be info online, or a simple phone call. You'd get a definite answer from the legal people instead of listening to yahoo's guessing and telling you it's fine. After all, I'm not the one paying the fine if I mislead you. :D
When I moved to California, I brought a motorcycle into the state that was well out of registration. That was many years ago so I can't remember the specifics but I do vaguely recall the masking me how I got it here. Since I trucked it into the state it was allowable.