I'm surprised that this piece of advice was not yet mentioned because it's the engraver's best kept secret.
Go to the store and buy a multi-pack of Pink rectangular pencil erasers. They must be the ones that are pink that have been around forever made by whatever that company is that has the monopoly on pink erasers.
Work over your gun's metal and engraving vigorously until you've used up one or two of the erasers.
The pink eraser gets hot and tacky from friction and will soften the grime and then whisk it away. The gun will look absolutely spectacular afterwards with no chance of removing any metal at all. It's amazing how something so simple can make such a big difference.
I had a drilling that was prolifically engraved a few years ago and when I got it everything looked shallow and lifeless. After I used an eraser for an hour the gun's metal looked as new and the engraving was back to the original depth after all the invisible grime had been removed.
The pink eraser trick also removes microscopic surface rust so the engraved channels seem to shine more, just as was intended by the artist's hand.
