7'6" min - 8' All would depend on how quiet the horse is and whether the interior roof is lined (e.g. If you have exposed roof ribs or not). Let us know what your concerns are and in what context and if we can help.
Rule 3.4 currently states, all horses must demonstrate a walk trot canter to the vets.
Tennessee walkers, Paso finos, and some other gaited breeds do not trot. But can and do do well in endurance. International rules stick ( or suitable gait) after any mention of "trot" in the rule book. The Australian rule book does not. Although I am sure it was an oversight on the part of the original rule book writers, that doesnt do any good when an over zealous ride nazi turns a Tennessee walker away from his ride since it technically doesnt trot.
Basically just asking you to email AERA and ask that the oversight in 3.4 be corrected to include gaited breeds. Especially if you are a business owner that potentially would be sponsoring or approached for sponsorship to do some of the rides.