This past several months I've been riding the single exclusively and doing more climbing. Most of the climbing is in the saddle with standing only on steep (13+% or so) pitches. My cadence will almost never drop below 60 on climbs and only then when I'm in my lowest gear (30-30) on steep pitches and depending on a combination of fatigue and the length of the ride.

Generally, I feel good after a ride, even one that might have 70 ft./mile of climbing, but I've notice that my glutes and hamstrings have been getting tight; twice I've crouched to pet the dog (I should get a bigger dog) and with a leg stretch out behind me started to get a hamstring cramp. This tightness wasn't the case in 5 years of riding the tandem; I'd cramp on long, hard rides, but that would be due to extreme muscle overuse when climbing.

Any thoughts on what's bringing on this tightness? I don't think my position has changed, but the setback required on my Adamo saddle does give the impressing of sitting further forward; I don't believe this to be the case, however.

The riding, itself, is fine. I'm getting stronger and recently recorded a PR on a 2 mile, 9% climb (VAM 823, 5.7 mph); while that's no great shakes I'm 68, 195 lbs so I'm not complaining.

Have you checked the saddle position?

Cramping and muscle tightness are two different things. Your muscles may be cramping simply due to the extra workload they're being subjected to and to which they have not yet adapted. Tightness is a loss of flexibility or range of motion unrelated to cramping.

As I've gotten older I've found I need to stretch a lot more in order to maintain flexibility and avoid tight muscles. My exercise regimen didn't really change but I noticed my muscles getting tighter. I asked my personal trainer about it and his answer was "You're not 25 anymore, you need to stretch!"

if you are climbing much more than with the tandem, then expect more workout of the glutes and hams. Especially if you're doing most of that climbing in-saddle and there are less 'breaks' in the uphill during the climb. Keeping a gear going, even at 60 rpm, requires a constant effort on anything above 2-3 %. More frequent changes to out of the saddle will help balance that.
Even riding rolling terrain in relatively big gears is not like climbing.
Keep it up, climbing consistent, longer grades is good for all of us cyclists.
Working flexibility and suppleness to those muscles will help a bunch. I'm a big believer in consistent/frequent self-massage ( if you can;t get some qualified therapist to do it) and, of course, yoga.
Being aware of on-bike posture, during climbs, can help to not rotate the pelvis backward.
its a good time of year to focus on posture during an entire ride and not worry so much about how hard/fast one rides...

First you need to determine if it's just being tight and sore or if they are legit cramps.

If it's cramping I'd make sure I'm staying properly hydrated.

If you just feel tight or sore, get a foam roller, do some mobility work, and see if things improve.

I'd agree with the above that it's just more work that's making you tight. The thing is, all this work is done within a relatively narrow range of motion for the muscles you feel getting tight. So they get tight. Static stretching helps some, but dynamic stretching helps more. My solution to this, because I have the same problem whether on tandem or single, is to add Straight Leg Deadlifts to my weight schedule. I use relatively light weight, about 50 lbs., and do 30 reps. You weigh a lot more than I and can use more weight. Low weight and high reps avoids problems with the back, but more particularly with knee joints and meniscii.
https://www.exrx.net/WeightExercises/...gDeadlift.html

Keep the barbell close to the shins as shown in the gif. Move smoothly. One could also use dumbells.

These will probably make your glutes and hams hurt more to start with, but that's how it always is. I also do leg sled and squats for glutes. Another thing that works the glutes more than one might expect is pedaling 120-140 on the trainer or rollers without bouncing, though that doesn't extend range of motion.

Even though this might slow you down a little to start with, you might also try spinning faster when you climb, around 80, at least until you run out of gears.