I don't think I'm cocking or bending them when pressing them in. I s'pose I could be wrong..
Here's how I do it:
I generally try to start the transmissions by hand, then set the barrel on a piece of MDF mounted in the drill press vice, and push the transmission in the rest of the way with the flat part of the drill press chuck.
You can sort of "feel" when it's going right. 14 years working on mechanical things gives you a good feel for when things are threaded correctly, and I think also gives you a good feel for when the press fit is right...
Does it make a difference if the transmission is retracted or extended?