Buzz,
There are more exceptionally skilled engravers in the US than you may imagine. In my most recent book, American Engravers-The 21st Century, there are featured numerous engravers who could do your project.
When you ask about "bulino" engravers it would be good to clarify a bit. Bulino is just the Italian word for burin or a hand pushed graver. Today, almost any finely cut scene or figure is often refered to as "bulino" engraving.
The technique used by the Fracassis and other famous Italian engravers is known as "puntini." With the puntini technique the entire scene or figure is made up of tiny dots that have been picked into the steel at varying depths and closeness to each other. Done correctly, the puntini technique can give a high degree of photorealism and yet it is the most fragile when exposed to casual handling.
Also keep in mind that when the engraver originally executed the engraving (duck), the gun was in the white, prehardened state. The gun then underwent the hardening and finishing process. On your gun, the engraver will have to obliterate the duck from the hardened surface then smooth the field to perfection then engrave the grouse into the hardened steel. It can be done but is much more complicated than the work that the original engraver of the duck had to do.
Many of the best engravers in America use a combination of fine lines and dots to accomplish a finely detailed scene or figure. While not technically true to the puntini technique, such work produces exceptionally fine renderings that are more durable than puntini and can more easily be seen without twisting and turning the gun to get just the right light on the subject.
Now, having said all of that, I will name some American engravers off the top of my head that can engrave a finely detailed grouse for you. Jim Blair, Winston Churchill, Ray Cover, Jr., Christian DeCamillis, Theirry Duguet, Eric Gold, Geoffroy Gournet, Lee Griffiths, Brian Hochstrat, Kurt Horvath, Jason Marchifava, Marty Rabeno, David Riccardo, Robert Swartley, and Sam Welch.
I have probably missed someone but any of those I named can do exceptionally fine "bulino" work. At the same time some of them may not want to get involved with destroying another engraver's work and replacing it with their's. Personally, I would rather begin with a clean canvass because of all the grunt work required before beginning to engrave.
Cheers,
Roger