This is going to work! Keep going!
As for pressing the worm on without ruining the motor... do you have a small jeweler's vise (like a Panavise)?
Just place the motor in there with the back shaft supported by one jaw, set the worm in place on the tip of the front shaft,
and then crank the jaws together. A Panavise is not a precision pressing tool, but as long as you get the motor set in
there pretty straight by eye, the shaft will tend to just follow the hole and go in straight without bending.
Another thing you can do... just use a 1.5mm chucking reamer in a pin vise (I think that shaft is 1.5mm, right?)
You can find such reamers pretty cheaply on eBay. The cheap $10 ones aren't great, but they will do the job for reaming out
a relatively soft brass worm. Just ream out the hole and then it will slip on easily with your fingers - no pressing required.
You'll need a drop of LocTite on the shaft before you put the worm on or it will slip, obviously. But the Loctite will
make it hold fast. Make sure you mark on the shaft exactly where you want the worm to end up, so you can slip it on with the Loctite
quickly. That stuff sets up very fast and you don't want it to get stuck in the wrong spot.