I don't know if it's viable for you (can you drive?), but in the country my mother often runs their three dogs beside/behind their car when she visits the cattle or horses in other paddocks.

This is only viable for her due to the remoteness of some of the dirt roads (so no cars), and the lack of prey animals in the area (they stop chasing kangaroos when called anyway).

That really is pretty shitty luck, but at least I can't see any problems with running your dog in circles. Only thing I can suggest is making sure he runs both clockwise and anti-clockwise- it's probably less important with dogs as they're much smaller and less affected by slight imbalances, but horses need to be lunged in both directions for balance and flexibility and it won't hurt him to change direction. If he likes fetch, that can also be pretty good as he's sprinting repeatedly while you're sitting still- you can get those handy toys that let you throw a tennis ball further with minimal effort too.