> you still need epistemology to tell you why you can believe the results of the experiments

No, you don't. This is a common mistake. Science is not about knowledge, it's about explanations. The whole idea of "knowledge" is just part of a vast web of explanations that turn out to be exceptionally good at accounting for the data.

> logical positivism

The mistake of logical positivism is the unjustified assumption that there exists such a thing as "truth", and that this thing is accessible to us by thinking. It isn't. It's a consequence of the empirical observation that the scientific method converges towards something. "Truth" is just a label that we attach to the thing that it's converging to (or at least appears to be converging to -- we won't know if that limit actually exists until we get there).