Polishing a lock is one of those things you start when you don't have anything else to do and time doesn't matter. You can do it all with sand paper or add needle files or needle files wrapped with sand paper, I prefer all three methods. You shouldn't get aggressive enough to remove cast in engraving.
Your second picture is of a casting flaw, it may sand out or you may send the lock back for a lock plate without the flaw, I understand the Chambers folk are very easy to work with, send them your picture and see what they say.
I polished this Chambers round face English lock (and a bunch of others), I think it took a couple of days but I only worked on it a few hours until my old arthritic fingers got tired and sore then I put it up for the day.