An update, but not much progress.
I haven't forgotten or given up: just busy. I had
regulators to rebuild, as well as other non-SCUBA items. This was not the best time for me to disassemble my compressor...
I have removed the intake and exhaust valves from the second and third heads. The instructions that came with the LF valves made this process very easy -- and yes,
@happy-diver, despite your condescending insinuations, I used the proper tool. No pliers were harmed in the removal of these valves -- and no valves were harmed, either. At no point was even moderate force used without the right tool in the right environment.
Currently, I am working on cleaning the heads and the reed valve. I will not be even attempting to clean them to the level that
@happy-diver has shown above: these are tools, not art, and they will get dirty the second they're put back into use. But I do have to say that his photos are motivating me to clean them better than I might have otherwise.
I'm backing away from even Crystal Simple Green: I've found that even at 1:30 a soak for a couple of hours badly softens the paint (not even anodized!), so I'm avoiding that. I'm going with Dawn Platinum and hot water, and an application of of nylon brushes, a 3m synthetic steel wool pad (gentle!) and brass brush (very gentle!).
Honestly, the biggest obstacle right now is fear. Inaction is easier than action, because inaction won't break anything -- and action just might. But inaction won't get this put back together; so I keep putting slow, careful effort into this.
Anyway, just wanted to let everyone know I'm still working on this. I'm very open to any specific cleaning suggestions -- no, more photos probably won't help. But if you have suggestions or cautions, I'm all ears.