It has been a warm dry winter/spring down here. Expect a fire ban around that time. Fire related forest closures are not common but can happen, so have a backup plan. Since it is a low snow year, my guess is that the Mogollon baldy trail #182 will be mainly snow free by early/mid May (although last year there was snow till June). Consider starting on the Catwalk trail out of Glenwood and following Whitewater creek to Hummingbird Saddle, and on to Mogollon baldy which will take 2-3 days depending on your pace. From there, there are many loops to be made. But avoid trail #102 over turkeyfeather mountain, it was obliterated by deadfall from a recent fire and looked very bad last year from a distance. Option 2: make a loop on the middle and west forks of the Gila starting out of the Gila Cliff dwellings national monument. You can hit the hot springs on the middle fork, and make any number of grand loops if you have a full week.
Also, for any of the routes along a creek there will be sometimes a dozen stream crossings per mile. Bring some well draining shoes.