My guess is that an evidentialist would say that pure priors are not justified, but gain justification as you incorporate more evidence in.

That sounds right to me, except that it's not really the priors gaining justification, it's the posteriors. Subtracting the prior from the end result wouldn't change the level of justification.

However, we do generally have a sense that some priors are better than others. Is that belief justified by evidence?

A tricky question. Our belief about a prior is different than the prior itself. So we may have a justified belief about a prior (e.g., we have evidence that we live in an ordered universe, so Occam priors have a head start), but we can't exactly "use it" on priors, because that just generates a posterior.

I feel a bit uncomfortable bandying about the word "justification" as if it's a useful primitive. As a label, I like "evidentialist" more for its immediate connotative value than for the final result of peeling through layers of arbitrary philosophical wordplay involving things like "justification" to see what we find. Evidence at least has a clean, useful definition under the Bayesian umbrella.