As another newb, found this interesting. I just bought an Omega and of course have watched the DVD several times and have also been on the T/C website reading about their solvent and bore butter, etc.
I immediately wondered what was so special if anything about Bore Butter. I figured that their #13 solvent probably had a water base in order to get rid of the corrosive residue in the barrel??
Although new to ML'ing I have done a lot of milsurp shooting using Yugo, Romanian and various other old Eastern Bloc ammo, all of which have corrosive primers. Our WWII ammo also had corrosive primers and I understand that military solvents of that period were water based in order to deal with the salt residue in the barrel.
The good number of the milsurp community use hot water down the bore from the receiver end followed by normal solvent cleaning and a lubed patch before storing. From time to time questions arise on using Ammonia. Consensus is that it's a good cleaning agent but doesn't have any special characteristics wrt corrosive residue. Nothing wrong with it, but soapy water will work.
The Cowboy Action Shooting community is big on use of Ballistol, originally invented in pre WWI Germany. Ballistol is an excellent preservative and cleaning lube. Black Powder Cowboy shooters often dump their spent cases in soapy water and initially clean their irons with hot soapy water as well.
Back to ML: After sighing in my Omega two weeks ago, I used a combo of equal parts Murphy's Oil Soap, peroxide and alcohol (store attendant provided this info where I bought my Omega - a long time ML hunter/shooter). This potion worked in spades, but I think plain old hot water followed by a good scrubbing with Hoppes etc will also work.
I used a Ballistol soaked patch as a last step in lieu of Bore Butter. Break Free would also be an excellent preservative as the last step.
This seems to be consistent with the other replies here.