but still had a tendency to freeze so quickly that the mixture stuck to the sides of the bowl and jammed the blade in place.

This is a sign that the freezing temperature of the mixture is too high, not too low. You need to lower it, so that it doesn't freeze so quickly. If you can get hold of some Xylitol or Erythritol you could use them. Xylitol would probably be easier for you to find, considering that according to Wikipedia "the largest manufacturer globally is the Danish company Danisco" which ought to make it easy to get hold of in Europe.

Technically of course, I'm not supposed to be using the Stevia at all, as it's still illegal in this country to use in foodstuffs *rolls eyes*
Seriously? That's nuts!