I've been using a Great Plains Pinion and Gear tool I found on Ebay for under $25 including shipping. Less than the cost of a new motor from MTH. Most times after the worm gear breaks free I have to put the base on top of vise jaws and gently tap the shaft the rest of the way out of the worm gear with a long punch. Desperate times call for desperate measures! LOL! But I've had good results.
I have one of those that I have yet to try on a worm gear, your post makes me think it might be worth a shot. I was a bit worried it would buckle under the strain.
FWIW, I'd be VERY careful about tapping on the shaft. That will frequently slide the commutator on the shaft and destroy the motor.
*** Update ***
The Great Plains Pinion puller does work! However, there are a few issues with the process. The 2mm pin that comes with it is too short for most worms. The other pin is 3mm and 4mm, too large for the 2.5mm shafts. However, it did break it free, and since the motor is already dead, I figured there was no harm in finishing it off with the punch to do the final push.
What is needed to make this a perfect worm puller is a new pin as below, the left hand side is 4mm, the cut is at 3/4 to 7/8 from the large end. The smaller end would be about 2.4mm and 3/4" long, that would handle a vast majority of the worms. The existing smaller side now is about 9/16" long, it needs to be a total of 3/4" to really do the job in most cases.