I have an 03 Mark 1 with what looks like a GI straight stock and a possibly repro handguard. I would like to rub the stock with cheesecloth and BLO as per the CMP. Is there any reason not to do this? Or anything better to do? Rifle is not bubbaed and has a 1942 SA barrel.

That works. BLO wipe on then wipe off.

If you let it sit too long on the stock it will gum up.  I let it sit normally 15-20 minutes then wipe off.  If wood it dry, oil it.  Afterwards I like to put a coat of howards on it.  When it comes to BLO, the rule of thumb is 1 coat a day for a week, 1 coat a week for a month, 1 coat a month for a year, and once a year for the rest of your life. 

The 1903 went well, but the Carbine is giving me issues. After 10 minutes the oil is bone dry and I can't wipe any away and it leaves it very glossy. Strange. I want to strip the stock but I cant 'destroy history'. Why is the oil drying so quickly?

I think the dryer it is out, the quicker that stuff dries.  if it is really humid out, I hear the stuff can take forever to dry.

 

When I did my stock, I just rubbed the BLO on, rubbed it in with a lot of elbow grease, and then wiped the excess off right away without waiting at all.  Then let it dry.  Best to not leave any thick layer on there.

 

And then after I put enough coats of BLO on there, a few coats of paste floor/furniture wax to finish off.  Came out really nice.