Grump,
Currently I am in the middle to end of browning a barrel myself. I would not use Birchwood Casey to degrease, as it requires a flushing of water. I would recommend going to the hardware store and purchasing a can of acetone, and using that. I use it in my laboratory at school for the same purpose when doing soil analysis. Trust me, it will take off everything without leaving a residue that brake cleaner might.
Second, I am using Laurel Mountain Forge Barrel Brown and Degreaser. It also has a degreaser built in, to aid in the removal of "accidental" fingerprints. The advantage of this over Plumb Brown is that it is a cold process. P-B requires you to heat the barrel (in sections) with a blow torch. You may not be able to obtain a even coloring this way. Also, the lugs to hold the barrel to the stock with the wedge pins are soldered on. You may inadvertantly loosen a lug - a very bad thing!
LMF is a cold process that depends on the moisture in the atmosphere to carry out the process, and takes a few days to a week to accomplish. I got lucky - right now, it is actually raining in Az. and that is helping my process out quite a bit. Read the instructions on the LMF Barrel Brown and previous postings/responses to my questions here, and you will know
what I mean.
You can get the LMF stuff at
www.trackofthewolf.com. They are very helpful, pricing and shipping is reasonable, and unlike a Walmart or such, they actually use and shoot the stuff they sell.
Good luck. So far, I've enjoyed the hell out of working on mine. I hope you do to also.
Matt