Also, it's my understanding that when most people talk about exercising for better sleep they are specifically talking about low intensity steady state cardio exercise.
You describe almost exactly what I face in training and I've seen substantial improvements in conditioning by adding rowing to my workouts. I actually do 45 minutes at around 19 strokes per minute at a 500m split of (average) 1:45. More recently I've moved to doing 1000 strokes per workout. That's at about 275-325 watts per stroke. I use an adjustable water rower with heart rate around 150-170 average. I get around 15-16km per workout.
The action is essentially resistive aerobic training, not unlike squatting as I mentioned. I can't say it'll work for you but I can say it's helped me find a form of aerobic exercise that maintains strength and conditioning.
Your height will give you a mechanical advantage but a water rower will give a non-linear resistive load so you can adjust it to give you the desired heart rate/wattage to sustain difficult training throughout the workout period.
Rowers are considered to be the absolute top of the pyramid amongst athletes in terms of balancing power/vo2 max/aerobic capacity etc etc.
Lifting heavy is the other part. Everyones biomechanics are different, so you need to adjust to fit your own, but being tall is not something unique. There are plenty of tall athletes who put on lots of lean muscle.
If you don't have a competition coming up (or if you are just training for health), then a mix between aerobic and anaerobic-alactic (strength, explosiveness) is much better.
Check my website [1] for the training methods that I usually recommend. For a non-athlete or someone in off-season I would stick to cardiac output, threshold training 1x per week and strength training.
You will see much better results and you will sleep better if you change your training approach. Hope that helps :)
[0] See Arthur Lydiard's work
Sidenote: I would recommend actually reading the tabata study. You can see that they also plateau'd after a few weeks (but the study duration was not long enough to see the long-term effects).