Fingers, your methodology isn't at question here. Iodine works but it needs to be cleaned off very quickly. It also makes a great Loc Tite when it dries.
The issue the OP has is a fully assembled rifle where the threads are buried "inside" the stock. No way to get penetrants of any sort into the area without damaging the stock. He needs to be able to get the screws to break free while the rifle is still assembled.
Kroil will work its way down the sides of the screw into the threads. I have never seen anything like it. Fill the screw slot with kroil and wait till it sinks in. You never touch the wood (not that it would matter if you did). Lather rinse repeat until you can work it loose.