stripping a Hoosier?

I just inherited my Aunt's old Hoosier-style cabinet. It appears to have originally been finished so that the original oak grain showed through, with a dark stain applied. Then 3/4's of the cabinet was painted at a later date.

I'm debating whether to strip the paint and refinish, or just paint the whole thing in a period colour. Any thoughts on which is best for value and "authenticity"? I'd always thought these things came painted and the sripping reduced their value - but this one seems to prove me wrong!