I painted my town home 7 years ago when I wasn't at all "painting savvy" and throughout my house there is dried paint on baseboards, window frames, etc. I'm now going to repaint the "proper" way, most likely hiring a professional. How do get all the dried up paint off the baseboards w/out ruining the wood?
Was the paint you dripped onto your baseboards a latex or oil based paint?
Was the coating that was already on the baseboards a latex or oil based coating?
I regularily use xylene to remove latex paints from oil based painted surfaces. There is no reason why it wouldn't also remove latex paints from a varnished or polyurethaned surface.
If the xylene dulls the gloss of a varnished surface, you could fix that by simply applying some "Wipe on Polyurethane" (the kind furniture makers use for their final coats) to a soft tissue and wiping that over the dulled area.