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I’m trying to change out the back of my watch because the glass is cracked, but I have a feeling I may might have at least partially stripped the screws even though I have the right driver… How easy is it to strip them, and how would I go about removing them if they are?

I can tell you that very easy. It seems that they use a locking glue and sometimes they may have been over screwed making them more difficult to unscrew with the result you have seen. I striped 2 , the other 2 got out easily. So even with a good tool, it will happen. I am waiting for tools to take both out, and ordered 4 new screws. Will see if I have success. The screws are flat inside, if your special screwdriver has a point that could be a problem. Mine is flat point but even with that type two of the screws did not came out. Good luck.