Robert,
When browning we are converting iron to iron oxide. Iron oxide takes up four to five times the volume of the iron it is replacing so when we card we are whacking-off the tops of tall crystals of iron oxide so the solution can get down to the surface of the part. I think the root of your problem is in technique.
First a clean barrel is necessary. I have been using Dawn dish detergent and water for years, on Getz, Rice, Hoyt and Colerain barrels, to degrease the barrel. I usually wash with hot detergent/water mix two or three times before browning. I use a browning box which is just a plywood box long enough for the barrels with bowls of water sitting in the bottom. It helps to put a cotton rag in the bowls to wick the water up. I use cotton flannel patches to apply the reagent in a single swipe per flat. After about 6 hours I card the barrel with either burlap or a small square of wool blanket material. Remember that chemical reactions are temperature sensitive - the reaction rate doubles with every 10 degree C (20 degree F) increase in temperature. I card after every application of reagent. I generally don't see much change in color for the first 3 or 4 reagent applications - just a hint of rust on the carding stock. That's OK, the base of the steel surface is getting a fine oxide coating - small dots of iron oxide across the surface of the unoxidized steel. With subsequent application of reagent more dots form. By repeating the process we gradually fill in the spaces between the dots until there aren't any spaces left. I think you have to card between each application of reagent to get results. That's what I have always done - I never tried skipping the carding part.
I don't think it is necessary to sand the barrel down. Just wash it real good with detergent and water and card after every application of reagent.
Good luck!
Best Regards,
John Cholin