How to best transfer power at 90 degrees for high torque applications
There are plenty of gears designed for 90 degree, search bricklink for "technic gear bevel" and "technic gear crown". There's also the "technic knob wheel", that seems to be used a lot outside technic, but I have a feeling that goes badly with a motor.

In my building the only application for worm gears is to gear things down, with regards to to size you can't beat the solutions it offers. But you're first gearing up to then gear down, that looks silly.