Smoke-pulls and/or pics are good for a 'picture' of the engraving.
A 'pull' is the most usefull in laying a pattern, or large missing piece of it back down onto the metal to cut it & reproduce the engraving.

If only small areas of the pattern are thinned out or missing, a picture or smoke easily lets you see what needs to be hand drawn back into place and cut.

Some engravers don't or won't do any metal polishing/ so the bbls may have to be sent ready to cut. They'd appreciate the above in some form to fill in any vague areas.

Others will work with you and on a job like this may even prefer to have you leave the last inch of the breech unpolished. That way they can re-cut and polish/blend what is there w/o any guesswork.

Do your Re-rib work first,,then polishing, then engraving recut,,then rustblue/brown or damascus finish.

Depending on who does it, and how they approach it )polishing work involved or not), prices starting at around $200/250 for the re-cut work(border and lettering).
Up, and way up from there.

Plus shipping both ways,insurance of course.