Based on what you've described, it sounds like the catch isn't installed correctly. You're pulling back, but the catch isn't sliding up and over the back of the plunger rod, and catching. Or the catch spring might be missing, or slipped out of place.
I could be wrong, but it doesn't sound like it has anything to do with the dart tooth. The dart tooth is in front of the breech and prevents the dart from being pushed out of the barrel during the forward priming stroke. If it wasn't working, the darts wouldn't stay chambered, and they'd just fall out the front of the barrel.
Disassemble it again, make sure the catch is moving freely in its track, and the catch spring is on its post and pushing straight up against the shell, then carefully put the top shell back on, and screw it together.
Now, as far as the spring being too long, it's not. Unlike the stock spring, it's designed to be under tension in the deprimed state. Unfortunately, that extra pressure makes the plunger, rod, and sled want to jump out of its track during reassembly. Sometimes the trick is to reassemble while the plunger is half primed - or not fully forward and in a more relaxed state.
All I can say is it's tricky getting a plunger tube under tension to stay put while you reassemble. Leaving the stock spring in is fine. Hopefully you installed the "cylinder protection ring" (aka plunger pad) from the kit too.