you might be overthinking it. it's definitely possible without any extra long jumps (though stuff like what you described definitely helps and pulling them off can allow for more mistakes elsewhere), but there's some jumps that look like they might need a long jump but are actually doable with just a double jump. i think maybe one of the real issues with the sequence is just the level design being a bit obtuse, and it's not really clear which kinds of jumps are optimal to use where. one person on discord suggested an indicator for where you're supposed to use long jumps which would've been an easy fix but I think the level design really just needed more iteration that I didn't have time to do.
i did think about adding a sound cue for when the long jump is fully charged which would've helped with that issue of releasing too early. that's just something that never made it in, but i'm planning on doing a post jam patch and that's something i'll probably add in that.
for the problem of having to reach the cat in order to reset, there is actually a button to immediately reset in the pause menu. it's only there during chase sequences and there's no indication that it exists so i can't really expect anyone to know about it but it is there and should fix that problem. i need to think of some way to tell the player it's there, not sure what a good unobtrusive way to do that would be. maybe i'll just add a note here on the game page for now