Lowest I've done Rio Chama is 550cfs and hit some rocks, and that was in an unloaded duckie. Rafts seem to do fine in the 800 cfs range, and 800 has been the standard release rate the last two years, higher in April/May during run-off. Last week-end before permit season this year is April 24.
Only time I went to the Gila was for a summer monsoon flow. I was solo, didn't have any beta, couldn't find a self shuttled put in and take out, couldn't cross into AZ due to the road being washed out, saw too many rattlesnakes, and even got a speeding ticket on the way home with no paddling that day. So no, I don't know much about the Gila.