Bobby, there is a screw removal tool that is simply a reverse thread/tap that after you drill a pilot hole into the top of the screw you want to remove and screw this into the hole you have just made. It will tighten in the direction to remove the other screw. You should be able to get it at any auto parts house. When you put your new screws into the wood use wax (crayons or candle wax will work) to lubricate the threads for future removal. Bar soap kind of works but it does dry out.

GO CLIMB A TREE, TIM

I have used JB Weld and also epoxy to glue messed up screws to screw drivers to get them out.  I have also welded peices of rebar to stripped bolts to remove them too.   Might try that then use the screw extractor.

slotted or phillips? Slotted recut the slot with a dremel tool. Phillip's screw extractor or also called ez out

good luck

another thought if the butt pad is rubber, insert hack saw blade between butt pad and stock and saw the screw off. If all else fails you stated your intention is to replace the stock. Use a skill saw approx. 1-2 inch from butt pad to gain access to butt stock screw(holds butt stock to action)

Sears has a drill bit type of gadget that you put on your drill. It basically is backwards threaded and when you run the drill in reverse it pulls out the screw. I can't remember how much it cost but it will be used again, i'm sure.

"It takes 32 muscles to frown, 17 to smile, but only 3 for a proper trigger pull."

My simple fix is drill out the head of the bolt/screw with a standard drill bit, Remove the stock then take out the fastener with ViseGrips. Hope the new stock came with replacement fasteners. Soap is an ok lubricant in a pinch but not an anti-seize substitute. Certain soaps or wax will cause metal to rust or corrode. I always use a proper anti seize on firearms, (especially on choke tubes )<-- an expensive lesson learned.