Here is the deal, for the most part law enforcement does not care much about registration on a trailer.
If you get stopped you will probably get a ticket for no trailer reg, but I doubt that you would get pulled over for no trailer registration.
You have Colorado, New Mexico, and Texas to worry about.
If it was me, I would just risk it. If I got caught I would tell the LEO the truth and see if he/she would let it go, if not I would pay the ticket.
The fact that I am opinionated does not presuppose that I am wrong......