Personally, I don’t think the rubs on the radial finish merit a refinish. They are really prone to picking up rubs in that area… mine has a few small ones and I have babied it !!
I think you’d end up with more marks on that within a couple of months wear, and due to the shape of the case there’s only so much refinishing you can do before you start interfering with the edge of the lugs.
Similarly, the scratch on the polished part I’d probably live with rather than polishing and affecting the profile.
Ironically, from your photos, it’s the damage to the bottom of the case side that would annoy me the most, so that’s the one I’d be looking to remedy. Hopefully you got it at a good price to account for getting it fixed.