I really don't think this is an adrenaline burst. I don't think Rusty even has adrenaline, lol.
It's really hard to explain, but you know when you let a horse out to pasture in the morning? The type who takes about three to five canter strides, then puts his head down to eat. That's what happens with Rusty. The first time he decided to gallop and yes, we were going down a hill, yes, he started to trot, yes, I tried to shut him down and he didn't listen and then cantered sideways, and I was having no success in slowing him down so I let him go, he galloped about three or four strides, and then came back down to a walk and was fine. This time, he got excited about going on a new trail. We were about a quarter of the way into the ride. He walked the whole time at a good clip, but still, not excited or jiggy. The new trail is on a slight downhill grade, he began to trot, I tried to pull him in, he ignored me so I tried to turn him into a circle, he responded by doing a canter stride with his nose sideways, I opted to let him straighten out his head and go towards the trees. He ended up with his face in the bark of an old fir, but at that point, he was not going fast. Maybe he was at a really slow trot at that point. The trail is maybe 10 feet wide, lined with trees on both sides. He couldn't get up to any speed doing circles that small even if he wanted to.
He does really love trails and gets excited. In the arena, I need a crop (though I don't actually have to use it anymore because he's learned that when I ask for the trot or canter, he needs to give it to me or else the crop will come out). Some days it's a lot of work just to keep him walking! On the other hand, the moment I let him out of the arena to go on a trail, his head perks up, his walk speeds up, he is happy. So whatever training tools I use, they should be used on the trail. Yes, I need to continue to work on his training in the ring, but he won't act up there.
Will look at a kimberwicke.
I think much of what you describe about Rusty is what people say about a lot of Appalousa horses. IT is one reason why they have a reputation of being 'pigheaded'. But, out on the trail, their go walk out and get there attitude is so fine! A lot of appalousa horses don't see any purpose in arena work and will start to become very resistant to it, but do love being out and moving over ground. You should have seen those Appy's on the Chief Joseph ride; all day powering up and down hills, and always with ears up and ready to walk on!
Two things strike me, though, about the bolded portions of your post. That is that both incidents occured where the trail was a bit downhill. That may indicate that your hrose lacks familiarity with how to handle himself and stay balanced, with a rider up, going down hill. It might be worth some work on those hills, specifically. Doing things like asking him to stop part way down, and actually BACK up the hill a bit, then praising him to the skies when he does and giving him a totally loose rein for a bit.
You guys have to be able to trust each other. He has to trust you to let him put his head where he needs it to be, going downhill, and to move a bit faster if necessary to keep his balance. And you have to trust that he won't just fall from there into a total rush out of control.
I would suggest doing some hill work if you can. Don't have anyone in front of you, unless they are willing to stop and go slow when you do, so that Rusty isn't worried about catching up if you stop him midway. That comes later. Get him to slow half way down the hill, back him up. Do the same at the bottom of the hill, turn him around and go back up the hill, and down, and up, until he is just 'ho hum' about it.
The 10 feet wide is plenty wide to do a complete hindend disengagement, as long as you are going no faster than a slow trot. So, the minute he starts to trot unasked, you can get him to circle into a disengagenemt. If he is cantering sidways through this, then you are allowing him too much time to take over before shutting him down, AND, you are pulling too much sideways, and not enough upward to get him to follow that rein around and not leak outward through his shoulder.