One of the things I'm working on is faster G sharp - B flat transitions. I'm using the side B flat key. On my horn, both notes fully voice in tune well before the bumper hits the body of the sax. If the corks were a mm or so thicker I could play the transitions faster because my finger motion would stop sooner. But is it preferred that one learn to make minimum movements with the pinky (G#) and side of right finger (Bb) instead such that one does not fully open these keys?
I'd use the bis or 1 and 1 Bb fingerings in that case.
I don't believe that shortening key travel 1 mm will make any actual difference, even though there's a long tradition of people lowering action hoping for that.
Honestly I think the side Bb is mostly a holdover from the early Sax saxophones where there was no 1 and 1 linkage between the upper and lower stacks. As originally a flute player I have to say I rarely use the side Bb. If you listen to some virtuoso flutists you'll see that they don't seem too handicapped by the lack of an analogous fingering.
If you're trilling or something like that, how about just applying the side Bb to the G# fingering as is and not twiddling the ring and little fingers of the left hand? I'm guessing it'll be somewhat flat but if you need it to be so fast that you can't use one of the other fingerings then it's probably too fast to tell.