I had no info on Gye & Moncrieff either, but I'm digging up a fair amount of info over the last few months I've owned this one. Gye and Moncrieff were only in business at St. James Place in London for about 5 years, 1879-1884.
Gye and Moncrieff were both British officers. Gye a Lieutenant in the Artillery, and Moncrieff a Commander in the Navy. Both left the military, and decided to partner in making guns. They did as many small gun makers, and purchased barrels, locks, etc, and had the tradesmen in their employ assemble double rifles and double shotguns.
Gye died in 1884, and Moncrieff closed the company shortly after, and returned to military service. He volunteered to fight in the Zulu Wars, and after a year was released from military duty, and appointed Consulate General of several different North African areas. His last appointment was to the Sudan, and while traveling to Khartoum with an escort of 250 Egyptian soldiers, they were attacked by Madi forces and the Egyptian soldiers ran. Moncrieff's body was found two weeks later in the desert. The sad end to a long service to England.