Just a thought. Here's what I do. I have an old trailer plate I found laying around. From a pop-up camper decades ago. It is still reg'd to my name and address, but to a pop-up that no longer exists.
I put that on the TC & leave both truck plates on the truck. If I get stopped I will just explain the plate switching hassle each time the TC comes off. The fact that the plate is reg'd to me shows that I am not trying to deceive anyone. I'll also explain that they don't issue plates for TC's as they are just loads.
I doubt there would be an issue.