I use a variation of the Ed's Red that uses odorless kerosene or lamp oil and odorless mineral spirits (paint thinner). I remove grips, field-strip the handgun and drop the parts in the can for a few hours or overnight. All the crud, powder residue, etc., just seems to float off or wipe off with minimal effort. I fire up the compressor and blow excess solvent off the parts and re-assemble. The ATF remains as a film of lubricant/protectant that I supplement with FP-10.
I've got an old strainer that I put a coffee filter in and run the solvent through it to remove particulate matter when it appears to be getting excessively dirty and then back in the can until the next time.
By the way - I use nytrile gloves to prevent skin absorption of chemicals/lead residue.