I quit using BLC and here's what I do now. When I empty a keg, I rinse it several times and then fill it half full of an Oxyclean or PBW solution. After soaking for 1/2 hour or so, I invert the keg and let it soak for another 1/2 hour. Next, I hook it up to CO2 and the beer line and run a quart or so through the faucet. I let that soak for a few minutes and repeat until the solution comes out clear. I then rinse the keg several times and hook it up again. Flush the line/faucet with a gallon or so of fresh water and let it be until I hook up another keg. Once I'm ready to dispense from the fresh keg I connect the beer line and pull a couple of pints. This flushes out the water and most of the settlings from the bottom of the keg.
Every 3 months or so I do an acid flush of the lines/faucet using Starsan. After reading a post on Brewer's Friend, I'm going to try using a citric acid solution instead of Starsan. 10 grams/liter is what was suggested.