what actually works to remove paint from wood?

When it looks fine wet and goes patchy dry, that's usually leftover stripper or old paint residue in the grain. After stripping and scraping (with the grain), wash the wood down with whatever the stripper tin says to neutralise it - often mineral spirits or water - and let it dry fully before you sand or finish. New finish over residue never takes evenly. Older house: test the old paint for lead before you sand it or go at it with a heat gun.