Update 3/1
Today was our toughest day so far. Last night the wind was blowing pretty hard and we wondered if it would continue today: it did, only stronger. US 60 from Superior to Globe appears to be carved right out of the mountains, and the path of the highway forms a perfect wind tunnel when the winds are blowing in the direction they were today, that is, a direct head wind. 
After a good breakfast we started up the mountain, and the first three miles were the beginning of a challenging day. For those first three miles we averaged a whopping 3.7 mph, only occasionally being able to break the 5 mph barrier. The grade itself is probably about 6%, but added to this were the winds which I estimate at a steady 20 - 25 mph with frequent gusts of 35 - 40 mph. There is little if any shoulder most of the way, so it was nerve-wracking to hear the motorcycles (lots of those out for a Sunday cruise), cars, trucks, and RVs zooming up behind us and hoping they would move to the center to give us some room. Most did, although the RVs seem to think the yellow line is absolutely sacred and not to be violated for any reason.
Just before the three-mile mark there is the Queen Creek Tunnel, again with no bike lane or adequate shoulder, We put on our lights before entering it, and all went smoothly . . . slowly, but smoothly. We finally arrived on the outskirts of Globe at about 2:30 PM and paused for rest and a late lunch. We then decided to add on a few more miles in order to make tomorrow more manageable, so we rode another 10 miles to the Apache Gold Indian Casino where we're spending the night in a Best Western Motel. We checked into the motel just before dark after riding the toughest 34 miles of the trip so far.
We had some pretty good elevation gains for the day. In Superior we camped at an elevation of 2652 ft, and after 3 miles at the end of the tunnel we were at 3474 ft. About 10 miles from Superior we completed the long climb and topped out at 4614 ft. There were lots of intermediate climbs along the way, also. Needless to say we'll sleep well tonight. The winds don't seem to be as bad right now, so we hope that will continue tomorrow.