Lakewood BBM aluminum bell alignment ring question

The correct one in the kit is very tight on the trans side, and just as tight on the bell side. I have access to a lathe.

I would think it would be best to machine the OD to fit snug, then tap it onto the trans side as I install.

I don't want the bell side fighting me when I actually stab the trans/input.

Would this be the best way to solve?