What do you think is the best score a person with an over-the-top swing could get

If you can deliver the clubface to the ball consistently then you can score in the 70s with a shovel.

I'm been paired up with some absolutely horrendous swings over the years. But same path, same club face at impact, same start line and finish can equal good result.

I have a very upright swing that gets over the top. While this helps me play a fade, my miss is a dead pull left. Current handicap is 5.6.

If you have a repeatable swing and you can do it consistently, you shouldn't have any problems becoming a single digit handicap.

so many great golfers over the years have come over the top

Bruce Lietzky

LINK

Shorter: LINK

I am a 7 HCP, decent player, my natural shape is a draw. I can hit some really great shots but not always consistent. My misses are sporadic and can be big hooks that go off the planet.

I play with a few guys that hit short fades but I find myself jealous of them, because they have a swing that has the same start line, the same curve, and the same distance almost every time. Every once in a while they might hit a straight pull but it's few and far between and it's still not too far off the FW or green. They will shoot in the 70s often.

If you can start the ball on the same line every time, with the same curve, and know your club distances... you can be a really good player. You don't need to hit far.