Here are some photos of the homemade tool I use to remate the barrel and trunnion. This tool was made from 5/16 all thread rod with the peaks of the threads turned off to make it small enough to fit down a barrel. I took the peaks off in a lathe, but I am sure it could be done with a hand drill and a file.
You dont have to take off much.
Notice also that I use a fit up punch to make sure I dont go too far when installing the barrel. I insert the punch when the hole becomes big enough. I tap tap tap the punch in as I continue to slowly pull the barrel in. As the barrel pin hole lines up, the punch will get snug. If you watch the position of the punch in the hole on the far side of the trunnion, you can judge how close you are by how well the small end of the punch is centered in the hole.
These photos were of an AMD 65 barrel being installed after the trunnion was riveted to the receiver.