Tough question, while I do shoot the 38-55, it's in a singleshot and I don't use Black powder. I do shoot BP in 43 Spanish, 43 Mauser, 45-70 and 50-70. I recall that there was lots of discussion on the 38-55 and other 38's for long range and black powder on the old shooters.com site. Unfortunately that site is gone and so is the wealth of information that they had accumulated.
Your right about the blow tube, it works very well in a singleshot. It's bound to be difficult in a 336 action. Have you considered a wet patch instead of a dry one? Wet would be more effective (messy too) in loosening hard fouling. Better yet consider using lube formulated for BP shooting. SPG is good for starters and some folks like to make their own home brew lube, there are several pet recipes.
Try posting your question on the BPCR board, there are probably folks left over from the old web site that can offer the specific information that you seek. You should also check out your twist rate, barrel length and lube that you are using and provide that information along with your question.
see
http://groups.msn.com/BPCR