Reddit mentions of Foil Fencing: Technique, Tactics and Training: A Manual for Coaches and Coaching Cadidates

I may have misread the OP, but I don't think that the claim was that sabre is comparable to longsword, but that the differences between longsword and epee is about as much as the difference between epee and sabre. The weapons and their use are very different, but both can be taught within the same general framework.

As for a coach teaching you to move correctly - see my earlier post. A modern coach with no interest in HEMA will obviously not be able to teach you to move correctly for longsword fencing, but a modern coach who also knows longsword will be able to adapt their teaching style to train you to move correctly.

One thing that is tricky about fencing is that the way it is presented to students is usually different from the way it is presented to coaches, so if you've mostly learned within a club, you probably have less exposure to the theory and the pedagogy of teaching as someone who's been training to be an instructor. There are a couple of books that are written from this perspective that you might be interested in:

Understanding Fencing by Zbigniew Czajkowski

Fencing and the Master by Lazlo Szabo

Foil Fencing by Istvan Lukovich