As a rider with just one hand, standing up on the pedals is doable, but I can't transfer any meaningful power. On the road, I only do it for butt relief.

On a trainer, however, I can stand and lay down major power.

Since standing is not something I can duplicate in the real world, does it make sense from a muscle development standpoint to do trainer intervals while standing, or am I better off doing intervals from a position that I will use on the road?

I'd say on the trainer, perhaps. Sometimes being able to recruit another muscle for just 30 seconds will make it so you can get those extra precious seconds in a tough training zone during a set of work. Kind of making the power however you can to get the physiological adaption/benefit.

I'd go for it on the trainer if necessary.

My legs got a useful improvement in strength with standing intervals on the indoor trainer. It translated to seated pedaling outdoors. Go for it.

For that matter, a stair-climbing machine would work too. I wouldn't buy one, but I'd use one at a gym.

No. Trainer time is about allowing you to do more in the real world. If you can't transfer that, it doesn't help. You'd be better off using that time as you say. There's actually more going on here than it might seem. When I come back from a hard group ride, my arms and shoulders are tired. Why? Because I've been prying on the bars while i put out twice my FTP while seated, and I have what passes for a smooth pedal stroke. You can't do that with one arm. You won't be able to follow up a steep hill at those power levels. You are a little lighter without that arm and the upper body muscle that goes with it. Your strength will be long climbs. Train for those, ride them.

Be that as it may, it is said that in winter you train your weaknesses, in spring train your strengths. I'd work on putting out high seated power on the trainer, VO2max work, max effort work. Better yet, switch out the trainer for resistance rollers and make your training more like your experience on the road will be. I think that would be even more important to you than to the 2-armed riders.

I would ask myself "what are my goals" Is mid-season power and results the big one? Or is it enjoying cycling year 'round and taking advantage in winter of things you cannot do in summer? I agree with those above that you may not be seeing your out-of-the-saddle gains translate into big gins mid-season. I think you will get some gain but it is probably not the best way to maximize our mid-season form. On the other hand, if it makes winter trainer riding fun and puts spring in your step, if you will, and makes the long winter more enjoyable, it may well be a quality of life step up from not doing in and might be worth a touch of setback in the oh-so-easy to stay motivated summer months.

There are those who ride the velodrome in winter, XC ski or swim. All do not translate directly to mid-summer speed, but coming into the summer season with an active and disciplined winter is far, far from a total loss. And burn-out can cost any athlete far more than a winter routine that is not exactly specific.

So, no answers. Just stuff to think about. (I feel for you, I live to ride hills standing. I thank G** that I have always been able to. And I have had enough physical setbacks - and some big losses - to know I get to take nothing for granted.)

Ben