Techniques for jumping BPM

a) if you have a big BPM jump, one of the most secure way is to move it up if the slower track has no drums and the faster has drums only. Speed up the first track, mix in drums.
b) If if sounds bad, it is bad. In most cases a semi-tone scale step does not sound good mixed together with original scale but hey atonal music (like techno) works fine, drum only parts work fine, filtering helps out so there’s no definite answer. I know people always answer by some kind of fixed chart/algorithm but me thinks just experiment and if you know it sounds bad, you learned another thing.

If I go from slow to faster I do like the “echo loop” transition.
I hope I can explain it right:
I try to get the slow playing song in a loop on its breakdown (like a 16 bar loop) and put on some echo, then decrease the loop step by step (hear the beat) EQ some bass out and decrease down until you reach 1/8 beat loop. Then slam the new faster song in with crossfader and some low filtering and bring the filter down until its all normal and cut the old song out.
Works best if the 2 songs are “harmonically compatible” as the slam in of the second would produce a disharmony with the loop…
You can of course vary this transition a lot with other F/X, loop only down to 1/2 etc.

As far as keys on the Camelot wheel, there are ways to make bigger jumps. If you go up 2 or 7 on the same ring (inner or outer) it can actually create an energy increase, conversely you can down 2 or 7 and relax the energy a bit. I know Key =/= energy, but try it out and you will be surprised.

BTW, I did not come up with this technique, but I read it and gave it a shot with very pleasing results.