So I went to the store today for lunch and bought me a scotchbrite pad and some tongue oil. (Dang that stuff tastes nasty!)
I spent all last evening putting a 3rd coat of finish remover on, and then sanding the entire gun stock with 300 grit sand paper.
As soon as I came home today from work I used the tack cloth as suggested and removed as much of the dust as I could from the stock and the checkering and swivel screw holes, etc.
Here is what I have so far after 1 coat of 'Tung' oil, and then rubbing it down with a dry cloth after it dried a bit:
a close up of some checkering:
All in all I am happy with it so far, and can't wait to do another 8 coats of the Tung oil or so.
Thanks again to everyone for the helpful suggestions.