I, like most 44 Special fans, handload most of my rounds. I like a nice 200gr lead RNFP bullet pushing along mildly for Cowboy and general messing around practice loads.
When one of the 44 Specials is with me during hunting seaon or as a companion in the field, I use 240gra lead SWC bullets at around 900+ FPS. This is a great all around load.
The lead does not build up much as these velocities. When it does get to the point that it needs to be cleaned out, there is a product called Outers Foul-out II that is absolutely wonderful.