Denny, I have seen taps that were made just for threading inverted flare fittings, and they are just as you say, having a recess in the tip for the seat. I think it was Snap-On that had them, but I'm unable to find them in their online catalog. I won't see my local dealer until Friday, but if I remember, I'll ask if they still carry them, as I've been wanting to get a set of them myself.

Bill Burmeister