Vintage Omega Seamaster Cal. 562: Frankenstein Check

I've been looking to buy a vintage Omega Seamaster for a while, and finally bought on eBay what I thought was an original 1961 Seamaster (with a few fixes and non-original strap+buckle) - serial number, calibre, coat hanger S and other details made me think it was completely original

After receiving the watch I loved how it looked and was really happy with it, but wanted to double check that the case numbers I'd received with the watch matched up to the other details. I know I probably should have asked for this originally, but this is where issues started to crop up, and more searching brought me to this forum, which has so far been really helpful.

The serial number (1831xxxx) + calibre (562) both match to 1961, but the case number is listed as 166.037, which when searching seems to relate to Seamasters in the late 1960s. I can't find any examples of 166.037 that dates to 1961. The watch cost me £1.2k, which I justified because I thought I'd bought an original piece in great condition with service + warranty, rather than something put together from mutliple different Seamasters

I have a 30 day return policy, so it's not the end of the world but I'm currently feeling a bit silly and the more research I do the more lost I get haha

Any help / thoughts would be massively appreciated, thank you!

Photos + watch listing below:

Omega Seamaster (Pre De Ville) Automatic Watch

• Gold plated with an original silver dial, embellished with raised gold baton markers, gold hour hands, a sweeping gold second hand, outer minute markers and a gold outlined date window
• Gold plated case houses the highly reliable 562 Calibre Automatic movement which has recently been serviced
• Brilliant condition, very well looked after
• Serviced + 12 month warranty

The caseback and its raised engravings look very fresh and crisp, for an item which is supposed to be 65 years old. It may be significant that the seller's description omits to say anything about the originality of the caseback.

Thank you, makes sense. Unfortunately I don’t have a photo of the reference, but will contact seller to check this. Probably a stupid question, but what makes the extensive polishing an issue?

Thanks for the help everyone - guessing from the polishing that it’s not worth the price I paid?

Any advice for avoiding more ugly sisters and finding a Cinderella?

Any idea if this makes it likely that the case matches the watch?

Thanks Fairy Godmother!

And ask before you buy. The biggest mistake you see is the “hi, just got this in. What do you think?” Threads. They always end in tears.