Would it be a bad idea to press a barrel out just far enough to knock the rivets out and tap the holes, then press the barrel back in ( thus avoiding the need for a bottoming tap ). Does that put any kind of unhealthy stress on the trunion?
There's only about 1/4" of barrel left in the trunnion if you press it out that far. If you have the means to remove the cross pin and push the barrel that far, you might as well go the rest of the way and not have the barrel interfere with your work.
as Rhino_66 said you have not saved much by not pulling it out, HOWEVER their certainly is no real damage I could see by leaving it in a bit. Make certain you get all the chips out before you press back in. Also I personaly would spray in some lube before you press the barrel back in. If you want to do it this way I say DO IT then post back here and let evryone know how it went.
Another word of advise is to check for galling when the barrel pushed out, if you see galling then you may realy want to get it all the way out to sand off the high spots.
TRY IT and good luck,, BTW what barrel do you have?