Another loop we've ridden many times is starting in Show Low up Hwy 60 to Springerville. The downhill before S'ville is a beauty, we hit 53 mph on our tandem (coasting) and by the time we were up the other side of the big dip we were in our granny gear! Suggest overnighting in S'ville. The next day continue UP Hwy 60 past Greer and toward the Sunrise Ski Lodge and onto 260 for a swooping downhill toward Lakeside/Pinetop (very heavy traffic on a weekend) and back to Show Low.
You'll be up to 9,200+ ft if you make a detour to the ski lodge. Then grab a ride on ski lift to get you to the top of the black diamond mountain. Forever views!
Be forewarned, summer thunder storms are quite prevalent, so pack a rainproof jacket as the temp can drop 20+ degrees in less than 5 minutes. Just missed a hailstorm one year near Greer . . . big hailstones about 3" deep by the roadside.
A real stress on the lungs on that climb . . . 3 to 4mph in granny gear. My stoker/wife Kay has only 75% lung capacity and managed to make it OK . . . but we were younger (in our late 50s) then. This is not tandem-friendly terrain by any measure, but do-able.
Sounds like you'll be in shape for your Alaskan event S'Lizrd . . . good luck!
Pedal on TWOgether!
Rudy and Kay/zonatandem