I thought this was some special numbers matching transmission case? Why are you looking for the cheapest fix?
Not saying any of the thread repair options are that expensive but jeez.
Where on the pan rail is this screwed up hole? Is it one of the bolts along the sides where it pokes all the way thru or is it along the front or back where they are blind holes?
That said I've seen helicoils come out before, but I've done lots of them on trans pan rails (not just on 727s) and that's one application I've never had a problem with one.

Something that pisses me off though is ham fisted idiots that think everything is metric
Some years ago my son had to take a trans in and "have" it done, he took the trans out and took it in as a "bench job". The pan was pulled up on taking it out of the truck and put back wit only a few bolts as we knew it was coming back off anyway.
The trans came back with all M8 pan bolts holding the pan on, I had to helicoils most of the holes in that one.