I've been there! Still sort of there! :P
For some dogs, just laying there watching might work. For others, this will just make it worse as they get more and more frustrated watching the other dogs. With a dog that tends to over-arouse in the agility environment, you also don't want to teach them to stare at other dogs doing agility.
Regarding crating not being an option, it really needs to be an option. Dogs need downtime to relax and decompress, rather than always being "on" during the whole class. With a dog like this (and I have one) it is must easier to manage if you can do your turn, then put the dog back in his crate to relax. Preferably the crate will be covered will be covered, or in a car or quiet room away from the action.
Second option would be bringing a small bed or mat for the dog to lay on, but this won't allow their mind to really have a break as much as a crate.
Also working on the dog's entrance behavior. i.e. he needs to be calm and not pulling to get into the training space. This can be frustrating and take a long time, but once it starts to click it will become much easier as the dog knows the expectation. You can also break it up into accepting small steps of walking quietly, bust out the tug and tug him the rest of the way in there. Same thing on the way to starting an exercise. No pulling or barking to the startline. And this is where a crate really helps again, because if the pulling/barking is just out of control, sorry dog you lost your turn, back in the crate. This really helped my crazy guy.
You'll also need your instructor on board with this. As well as understanding that for a while, you might be paying for agility classes but not getting the opportunity to actually do much agility if you're not getting the calm behavior that you want. I had to do that for a while too. Sucks to feel like wasting money like that, but it does pay off in the long run.
Sorry for the long response, but that is really what it takes with this issue. No quick fix, just lots of patience and consistency that being a nutcase does not earn the opportunity to do agility.
Your other option is to be like Silvia Trkman and not care at all and just let the dog be a nutcase. Haha.
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