PVA seals wood, and wiping off the excess doesn't prevent that, so any stain
will penetrate less in that area and give you a different colour.
A stain based on a strong solvent might cut through the pva but these are
hard to come by nowadays. Naptha, toluene, xylene etc.
A tinted varnish, which is designed to sit closer to the surface, should
give you less colour differential.
You could pva the whole section where the problem occurs. Sounds silly, but
it would give you a uniformly less porous surface to work with. IME allowing
dyes to freely penetrate isn't a good idea anyway, especially the darker
shades.