First of all, there is nothing ideal about being done hiking and back to work by a certain date, ok? Come on now.
That settled, watch the weather this winter. Unless it's a gangbuster of an El Nino which now seems unlikely, then the southern ranges will (we hope) see the usual storm-every-week-or-two, bringing some light to moderate snow to the high country which will linger above 7000 ft on north slopes or maybe 8k on southern slopes. You'll be in and out of these areas within a day or less as you traverse the AZT in this region. Pack some lightweight ice walkers and an adventurous attitude, but skip the ice axe which would be overkill. Snowpack elevations will probably drop, and the frequency of storms may increase, as you make your way into the central highlands region including the Mazatzals. Once atop the Mogollon Rim near Pine you can expect (or should expect) to be walking on snow for some or much of the time en route to Flagstaff and then around the San Francisco Peaks, approaching GC south rim, and then from the north rim all across the Kaibab Plateau to nearly the Utah border.
Temps in the southern desert will most often be mild to warm by day, chilly to cold at night. Higher elevations, including the northern half of the hike, will usually feel pleasantly nice only when the sun is out strongly and the wind isn't blowing.
Or you could wait a month, start in mid-March, and have a milder hike and probably a less challenging one, at the trifling expense of work commitments.
