Also, string theory even today is speculative; a lot of physicists think it's a good theory, but it is experimentally untested, because nobody can think of a way to test it; we can run plenty of experiments that are consistent with string theory, but they're also consistent with lots of other theories. We don't know how to run experiments that will help us to distinguish between string theory and the others.

And in any case, the point of the model is to describe observations of electrons that we can make directly; those observations don't involve extra dimensions even if there are any. They directly involve the four dimensions we can directly observe, three spatial dimensions plus time, i.e., spacetime. Even if there were string theory machinery "behind the scenes", so to speak, it would still have to be describable at some level as electrons moving through spacetime.