I don’t know what your rig is but I assume it’s a big one since you’re asking about routes. You have a few options, Payson being one. The Tucson route is the tamest but it will add roughly 250 miles to the trip. You could also come down I-17 to 101 and 60 and go east into Apache Jct. Or you could come down from Holbrook through Globe and straight into AJ. That route, though, crosses Salt River Canyon, about 10 miles of switchbacks and drop-offs. Entirely doable but some people don’t like that sort of geography.
Crabbin cabin’s route works, too, it just adds mileage like the Tucson route. The stretch from Globe to Superior is a lot of two- lane and a bit tighter than the other roads and there’s a tunnel and grades and curves. But less so than the northern routes. The only thing I would add is both the Payson and I-17 routes can be a PITA on Sunday afternoon/ evenings with people coming back to Phoenix from the high country.