I would not round pen him if it were me. I think it will just build up his stamina, and make him worse. But that is me, others may disagree.
I would stick straight to basics, moving over when told, coming up etc. As for the backing? If you have tried this too, ignore it please.
How I teach backing is to run the flat of my hand down the face, until right where halter/caveson rests, and push towards their chest, at same time I am saying back. I give and release very slightly. I want the horse to move back off of head.
The problem to me with ponies is they are so strong for their size. Just little chunky fellows.
Also, if this pony is at their place, they may undo everything you teach. And they are with it more. What, also are they feeding it, as that can have a lot to do with what you are seeing.
We had a TB filly, that went flat every time she saw the farrier, she never offered to struggle, just laid down. He did her like that, but it is not a good thing.
It could also be with the round penning, that he gets so mentally wound up, he just shuts down mentally, which is another reason I would not do it.
Try just working with him in ways that don't involve that. Ponies are tough little creatures, and it may be a calm, quiet method will work better, where you seem to be in complete charge, than him racing around pen.
Make sure you are having same space rule with him at all times.
But again, if they are going out there and playing with him, as I imagine they might be, when you aren't there? You are not ever going to get anywhere.
And at only 10 dollars, you are losing money I think anyway.