Yes, that would be the best way I would think. Unfortunately, the transmission is back together and I would not want to risk any filings going AWOL. :)
Just pack the tap with grease and tap it slowly. There is no drilling required. The set screw and tap size is 3/8-16 and I start off with an 1/8” orifice. The other thing that you can do is use a shop vac while tapping the hole.