This link has several ways to refinish stocks most are used when finishing multiple stocks but the results are hard to beat. The Gunsmiths :: Log in
If your going to bed the action you don't need to finish it, the bedding material will seal the wood.
Before removing the finish try rubbing it down with 0000 steel wool it will remove the shine. To remove the finish you can use a paint stripper, Brownell's sells several good ones, it won't affect the checkering if it gets into it just use a tooth brush to remove any finish in the checkering, If its a hand checkering job a checkering oil is used to protect it.