You're on the right track. Please stick to the concessions that operate remote from 7-Mile. The beach is not a safe place to ride... trust me, I've seen things. And, in general, the beach is NOT a safe place for the animals, either. If you're staying on the beach, you'll see what I mean.
The animals are not well, nor are they treated well, with no protection from the heat, and little in the way of fresh water. Chukka, as I understand, has a safe operation near Negril... a bit north of the strip, perhaps 10 miles (?). I've not heard of the other vendor.