Since this watch is starting to get interest, I suspect it will sell for more than I can afford, and I wanted to share the original plan with you.
I have two KO 2627 watches.
The watch on the left has a decent case of average quality as seen today. The lugs still have facets but the edges have been polished away. It has an OK 353 movement, the crown is a replacement, the crystal is a modern replacement, and the dial is only average. Not unattractive.
However... the watch on the right has a very good dial, a good 355 movement (but not perfect), the original crystal, which is domed, and the original crown, which has a tall skinny Omega symbol. Its bezel, however, is heavily polished.
The plan is to service the 355 movement (and I have sourced new parts for that on behalf of my watchmaker), and swap the cases. Use, if possible, the original crystal and crown on the better case with the 355 movement with its dial and hands. Normally I am not a fan of the magnifier on the crystal, but it's original.
If a miracle happens and I can buy the better watch, these two will be for sale, but if it goes how I think it will... this will be the plan.