But I don't want to remove the caps again...making sure the springs are aligned in the first place is so tedious
Ha Ha Ha Ha Ha
I assume that all the caps will come off and on at least twice during every mod project, usually more. Once you get used to it, you can do it with your eyes closed.
If you are careful to keep the stem centered, and use a top-down rocking motion, it is really not so bad. Also, it sometimes helps to tip the keyboard up on the front (spacebar) edge to make the springs flop downward.
One word of caution: if you cut the floss too long, it will prevent the spring from seating at the top of the stem.