So sad to see such neglect.
If keeping it original is important to you then I guess you should leave it alone but obviously that pitting bugs you.

I've got one of these which was pretty bad too and my choice was to do a full resto which meant losing the etch but I had it re- engraved later. Not quite the same... but for me customising was acceptable.

Grinding too deeply on side sounds a bad idea tho.
Maybe some more folks have other options for you.