Before you give up on desert camo, you didn't specify which Iraq war. Desert Shield/Storm (1989-91) apparently came during the color scheme changeover for USMC copters. The book "U.S. Marine Corps Helicopters" (Concord Publications, 1993) shows Marine helos in Kuwait in virtually all schemes, including presumably temporary desert camo:
all sand - AH-1W, UH-1N;
sand and grey-green - AH-1W, UH-1N;
sand and tan - CH-46E;
green/grey/black - AH-1W, CH-46E, CH-53D;
solid green - CH-53D;
all-grey - AH-1W, UH-1N
Cobras and Hueys in the sand schemes carried only a nose no., no national insignia or other markings. Those in the new grey added the BuNo on the tail.
Once these A/C returned following the war, the temporary and outdated colors were replaced with solid grey. Sorry, I don't have dates.
Regards, Dick