Chain snags on larger cog

MartyZ

I just finished restoring a 20+ year old Centurion Accordo. I put on a Shimano 105 CS rear derailleur, which is supposed to be 6 speed compatible. Anyway, the first 10 miles or so everything worked fine then I started feeling chain slip. Let me just say that the bike has the original 6 speed Uniglide freewheel, the one with all twisted teath(by design for easier shifting). I picked the bike up and turned the crank by hand and noticed that if the chain was on any cog other than the largest it would momentarely snag on the top of the larger cog next to it. The shifting is correct and it shifts fine to the correct cog, but the larger cog snags the chain and drops it, snags it and drops it, and so on. Could this be caused by the chain or freewheel. Let me just say that it happens the chain is any cog accept the largest, obviously, and if it was a freewheel problem than it would mean that all the cogs are bad, is that even possible?

Any and all help is greatly appreciated.

One other question. If I do need a new freewheel, can I replace my 6 speed with a 7 speed, or will I need a new hub?