You load and fire the rifle yourself, and you'll be cleaning it yourself, too, so a little maintenance should be something to consider doing yourself, too. The hardest part is waiting for the browning material to arrive at your doorstep. It's easier than waxing your car, and safer than shaving with a blade, and no more difficult than cleaning your rifle after a trip to the range. But once you have a taste for the fact that you've done it yourself, more projects will present themself for you to build or finish.
Over the past 40+ years, I've only used Birchwood Casey's Plum Brown or more recently, Laurel Mountain Forge's Barrel Brown and Degreaser.
Both provide a good brown finish, and you need a little more self confidence than actual skill to roll up your sleeves and get to it :thumbsup:
While the Plum Brown needs a little more care in degreasing the barrel before application, the Laurel Mountain Forge is a little more forgiving, and degreases while it browns.
If your current brown is coming off as easily as you mentioned, complete removal with fine steel wool & kerosine, followed by acetone or carburetor cleaner for a clean surface should be quite easy.
Track of the Wolf, Midsouth and Midway, among others should have either in stock.