After two failures in securing a DW-5600C in good condition Frankly I had lost faith in many Ebay listings afterwards. Surprisingly one popped up on Ebay right before I went to bed at 2:00 AM in the morning one day, and I didn't think twice and bought it. This time the seller was so much more responsive and nicer, and the 5600C he listed was described as in mint condition. I immediately asked him about the bezel screws and he said all 4 screws were intact. This 5600C I just got has the Japan H module 901.
10 days after the auction my 5600C arrived at my mail box, and when I opened the package I was very impressed. First of all the entire watch looked like it just came out from the factory. The mineral crystal was spotless!!! The bezel was new as the seller was also kind enough to send the original (slightly worn) bezel to me. The strap had a few scratches but this is no problem as I could also order a spare one online. The screw back case was scratch-free. All the buttons functioned properly, and they were not stiff! Finally, the light shrined bright and I think the alarm worked perfectly too.
Several differences I immediately noticed were first the watch was significantly heavier than the 5600E. The 5600C was a lot thicker as it had a screwback rather than the 4 screw flatplate back found on the E version. Also the module seemed to be a bit clearer and more crisp than the 5600E so it might be easier to read in some conditions.
Overall, I am glad to have finally found a 5600C in excellent condition. The 5600C for me is the holy grail of the G-Shocks. I am satisified for now, and I will probably buy a spare bezel and strap for it. Meanwhile, the 5600C will remain as a collector's item and I will only bring it out when the weather is fair. The 5600E will remain to be my daily watch. Not sure about the Japan A 691 module 5600C I bought earlier, but if it can be fixed I will do so in the future. But two broken bezel screws is no easy fix... Last picture is my 691 Japan A module 5600C.