Martin,
I don't even try and neutralise the browning agent. I've used LMF before and have gotten very good results with it. I leave the barrel in a humid area, when showing signs of rust the next day, I lightly card the rust with 0000 steel wool and then apply more browning and repeat the carding on the same schedule.Keep going until you have an idea of the color and quality of the browning, I then oil it down pretty heavily with motor drain oil. The used motor oil contains lots of hydro-carbons and will give a more black color to the browning. It will continue to rust for a while. Just keep oiling. You can always knock it back with steel wool and oil if done lightly. This will give you a very durable dark fine grained brown finish, much thicker and more durable than a Plum Brown finish.
Dave