I bought and partially restored a DW-5600C back in September. I really should have posted something about my experience then, but better late than never!
I had been looking for several months for a 5600C for the reasons most people cite: its a classic, solid stainless steel construction, screw back, easy to read display, flight qualified by NASA, … I decided to find a later (901 module) version so it would be slightly newer and take the readily available CR2016 battery. Given the issues with resin decomposing, I also decided to find a raw module (i.e., with no bezel or strap) rather than find one that had original resin that might fall apart soon after purchase. I planned to start with fresh Brazilian resin. Lastly, I wanted one that had all four bezel screws removable and not broken off in the case.
After a few weeks of looking on xxxBay, I finally found exactly what I wanted. I ordered it plus the Brazilian resin and strap. From the xxxBay photos, I knew the crystal had a few scratches, but when I got it I decided the scratches weren't all that bad so I didn't do any restoration to the crystal, hence I consider the watch partially restored but still in very good condition. I did however take the module out of the case, clean up the complete case, clean and lubricate the pusher o-rings, and put a new battery and caseback gasket on it and new springbars.
I'm very pleased with the result. It's a great watch -- very functional and good looking. I bought it for wearing not collecting! The alarm is loud enough for my needs and the illuminating light more than sufficient for the situations I use it in (reading the time in pitch blackness). The only thing I wasn't initially satisfied with was the accuracy. It was running about 22 seconds / month slow but I was able to easily adjust that. I'll have a subsequent posting on how I adjusted it's accuracy.