...there are a variety of folks who offer movement engraving for a fee -- the Habrings come to mind here with their "Carinthian" engraving options.
PSM added engraving of the automatic winder base plate on my Shimoda as a no-charge option when I bought that (now lamentably departed) watch.
Of course, if you pony up for a watch from some Independents (Kari as a prime example) you immediately enter into an enjoyable consultation on multiple aspects of watch design, which can include things like striping vs. frosting for plates and striping vs. black polish for the balance cock, for instance. That's all part of the (often hefty) price of the experience -- but here we are talking about paying a premium for tailoring, not the idea of good-better-best options for finishing quality.
An intriguing thread, as always with you, Andrew!
Best,
Gary G