Okay, so here's the catapult holy grail: I've often, for reasons I'm not sure of, gotten shorter catapults. Maybe angle or timing or direction. Has anyone found a way to make them longer? That would be huge.
Did preliminary investigations on Switch: using the same technique, catapults are MUCH shorter on switch. Freya's house takes you to the middle of the Grove, Poppy's house takes you to the middle of the Woods, and as far as I can tell it's impossible to jump into the city. Maybe there's another technique or timing, but it looks a lot worse for the route.
Okay hello here are my findings My partner Twelve and I found the catapult glitch. Normally, with precise timing, it shoots you directly to the opposite spot on the map. If we say the cafe teleport spot is 0, 0, 0, I believe it changes your position from X, Y, Z, to -X, -Y, 0 That means I can calculate jumps with just a ruler, and have done so, with a lot of accuracy. However, if you wind up below the ground, you usually get shunted off into the nearest ocean, so many spots are no-gos for catapulting. I have not personally seen any difference with direction or angles or party/cafe, but I may well be wrong.
That's when it's performed normally, with the timing in this image, as you're sliding off the side of the animal https://imgur.com/a/0Mk6Wx4 It IS possible with other animals, the timing is just more precise. I do not believe it is possible with the broom, because it has a different dismount animation, though obviously that would be huge.
I definitely have a number of cases of it not 'pulting as far, but I haven't gotten them consistently (and haven't explored it as I do not currently have a use case for a short catapult). It also looks like the switch version gets less distance than PC, which I'll explore soon.
As for catapult locations: My preferred for witching wood is halfway between Poppy and the nearest tree to the east. That deposits me in or around Rosa's house, very close. For Daisy, you can get directly to her with the trees near Freya's house. However, I don't use that. The broom is faster than the cat, so it's better to get into the woods and on the broom fast rather than taking the comparatively slow cat. I'm working on precision with the final clip, the giant cat, but my best so far is just up the road into the mountains, nestled right next to the first tree. If you go from the far end of the witching woods, you can get to the field outside the city. It's significantly slower than the clip, but it's worth keeping in mind.
As far as I can deduce from experience and a ruler, there aren't any more useful clips to the current route, just Rosa and big cat. I don't believe there's any way to get to Autumn, Lumi, or Xin directly, even if it were faster.
(As a side note, here's an easy time save I haven't seen much: there's a "toggle run speed" button bound to right stick on console and to nothing on PC that makes you always run at top speed, no windup)