Any way to make this setup "tighter"?
There are 2 ways to get it tighter. First is to use the new worm gear part:
http://rebrickable.com/parts/15457/Technic-Worm-Gear-2-Axle-Holes

The other is to use an axle with stop. Have the stop on the end which has the worm gear pulling it in. Not sure which end that is, so experimenting would be your best bet.