I would say that empirical truths (obviously not mathematical or abstract truths) are statements about an efficient model that seems to agree with sensory data and predicts incoming data. That's pretty streamlined but hits the biggest points, I think.

I don't think it reduces the quality or scope of philosophy if one doesn't assume a soul/immaterial mind.

Assuming unnecessary things to explain phenomena does, on the other hand, usually have negative consequences. Every one of your postulates is like a filter through which the truth must pass. More/stronger filters means it's more likely that the truth snags on one of those assumptions.

Sure, but ya know, Occam's Razor. Why suppose the brain is the middle man to an unseen object when treating it as the final object works fine?