How to get up deck boards with rusted screws, want to plane and reuse the boards so the screws have to come out
You could try heating some screws with a sodering iron until the wood smokes.  Maybe the burnt wood will be less grippy.  Let them cool back down before you try getting them out.  Not sure the cosmetic outcome from this will be better than your drill scheme, though.
Could try a blob of penetrating oil on top of screws and leave it sit overnight.  Maybe slippery wood will be less grippy.  That wood is probably thirsty after 25 years and the oil should soak in ok.