You are a little confused. First off, your 127/4.7 Tominon cells -- the front cell
is engraved Tominon etc., isn't it? -- are in a barrel made for another lens. So you're right there. And if the barrel is on a board with a hole drilled for a #0 shutter, well, then, it is a #0 sized barrel. Go here
http://www.skgrimes.com/products/index.htm for a handy table of sizes. Then measure, and you'll know for sure what you have.
The MP-4 Copal #1 press shutter has no diaphragm, is intended to be used with lenses in barrel made to screw into it. Its front threads are M40x0.75. Your #0 barrel, if it is a #0, has mounting threads M32.5x0.5. Since the MP-4 shutter has no diaphragm, putting lens cells into it except to check fit makes no sense at all.
I gather that you can't get the Tominon front cell out of the barrel its in. If all else fails, grab it gently with needle-nose pliers. I've extracted a recalcitrant front cell from a Schneider barrel by wrapping a rubber band around it ... But the front of the barrel came with it and the diaphragm assembly came out too. Reassembly wasn't easy. So be cautious.
Finally, the 127 Tominon isn't the best lens for 4x5. It is a tessar type, just barely covers the format. I shoot one on 2x3, where it works very well, but with 2x3 coverage isn't an issue. The big surprise about mine is that although it was made to be used as a macro lens -- it came from a gel cam -- it shoots well at distance.