I bought a 640-1 from center fire systems when they had them. Mine was like yours in that it's in nice condition-except that the extracto rod was chewed up. I replaced it,it's really easy. Midway USA has a video on how to do it. As far as the end shake issue I just put a new extractor rod on my new to me model 66 that I thought had excessive endshake,and added the 2 thinnest shims. It definitely helped. The best way I can describe what it did for me was that it didn't really reduce the gap- it just stopped the cylinder from moving back as much and making the gap bigger.
It's easy enough to remove the rod that you could try removing some shims and reassemble it and check. Just don't tighten the rod really tight until you get the final result that you want. Not a gunsmith or even an internet expert but this was my experience. Hope it helps a little.
Tad