Jon, I checked out that link you posted, sounds interesting, makes me wonder why it is recommended for interior only.
The problem I have with a lot of finishes is the fact that they dry to fast, makes it hard to get the finish around your carving and moulding smooth before it starts getting sticky. I don't like to use steel wool around carving, it gets down in the lower recesses and gets stuck. Then also you end up with light places where the steel wool cuts through the stain,no matter how careful you are. I put the finish on as light as I can around the carving and rub it in with my finger and the palm of my hand, then I use a toothbrush around all of it to get any puddles out of the incise lines and go over it again with my hand.
I hope you don't have problems like that on you Haines rifle because once you have its hard to straighten out. I have never used the scotchbrite pads,but they may work around the carving fine. Jerry