Darrin some horses are not capable of keeping up with some other horses. My horse for example, CANNOT walk as fast as my friend's 16.3hh Thoroughbred. He also CANNOT maintain a trot slow enough to keep pace with the same mare. He can do a western pleasure type jog for a few strides, but he is not physically capable of maintaining that jog for any decent amount of time.
The same applies between my non-gaited Anglo Arab and Mum's gaited QH.
Perhaps if your horse is getting jiggy when a horse trots up from behind, you should train it NOT to get jiggy? It's easy enough to do. Just get someone to trot up behind you constantly until your horse stops reacting. Your horse is training you when you allow a reaction to what other horses do. Your horse should be focused on you and it shouldn't matter what other horses do around it.
Yes, I have the same issue with my horse, he doesn't cope with horses overtaking him and trotting or cantering off ahead. I don't avoid the issue, nor should I. Indeed I embrace it, I view it as a challenge and all part of the fun!
You being a gaited person I can understand how you don't necessarily get that non-gaited horses don't have in-between gaits so that they can go at a speed between their maximum walk speed and their minimum trot speed, but it's attitudes like yours where it's always the other person's fault when your horse breaks gait (and not a training thing) that really irritate me. You wouldn't ride with me, because my horse doesn't gait. I wouldn't ride with you, because I don't like being blamed for things that I can't do anything about.
For the record, I have a friend who gets REALLY annoyed if I trot when she's walking. This is the same friend who has the big TB my horse physically cannot keep up with. I told her to deal with it, because there's nothing I can do that will make my horse walk faster. He can't give any more than what his body will let him. I offer you the same. My opinion is that you should train your horse better to cope with perfectly normal things like a horse trotting up behind it! All issues with jigging are training issues, not "oh it's just him" - the problem is that the horse is allowed to do it and it stops the trotting up behind so the horse learns that the jigging is a way to get what it wants - which is of course for no other horses to trot up behind it!
Yes, some gaited horses are hot. My horse can be hot too. It doesn't mean they can't be trained.
Control your horse's behavior so that others' behaviors cease to be an issue.
My horse balks at leaving a group or being left behind. Well, I want to be able to do both. So occasionally I set up a situation where she has to deal with it. When she starts to get upset she gets enough leg and enough whip to get over it and do what I want.