There seem to be quite a lot of worm gear sets available but none that can fit onto a 5mm stepper motor shaft.
Does anyone know of a worm gearbox that can be fitted to a 5mm voltage shaft?
Are there any easy ways to adapt the shaft to fit the plastic worm gears available?
There is lots, but mostly, they come with both input- and outputshafts, while for the Tamia, the worm is pressed onto the small diameter shaft/axle of the motor.
To use the mentioned two together, either get the shaft of the stepper turned down to the right diameter for the worm (hard, I wouldn't), or make a shaft coupler from a brass tube about 20 mm long or so, 7..9 mm outside diameter, with an inside diameter fitting an axle that fits the worm. Then drill half the tube up to 5mm, and drill and tap holes for set screws.
You might wanna take a look at Vex gears as well, they have a 20:1 box that seems far stronger than the Tamia parts and you can build one yourself with up to 60:1 in one "go". You can add some of course, 2 of the 20:1 in series will give you 400:1.