Forgive my lack of familiarity with the neutral electron prediction,
but does it mean that Heim's theory predicts a particle with the same
mass as the electron, but having no charge?

Hmm, but where would such a particle reside? Certainly not going to be
orbiting the nucleus, if it has no charge. Nor would it have a strong
force interaction to trap it in the nucleus.

Perhaps the neutral electron prediction is just some 'trivial solution'
which is just a manifestation of something else, as you say.