I also prefer to have some queens to fall back on if things don't go well, but when I do the queen in I dump her in a jar of alcohol. After you get a lot of queens it there, it works as a good swarm lure for bait hives.
I haven't every tried squishing the old queen on the new cage, but then I seldom have had acceptance problems either. Only really hot hives and laying worker hives have ever been a problem. Then I find a nuc with the queen on a double screen board for few days and then a newspaper combine usually will work.