So what did you find out? I've been out of Pinto for a while, so no longer know who exactly is doing what breeding wise with Hackney lines/PtHA.
I had 1 Hackney mare that I bred to a larger shetland stallion for 5 - 1/2 Hackney mares. None of them has the extreme motion that would do well in the ASPR or Pinto Pony, Saddle type, classes. But they did awesome in CDE driving and jumping!! Bred back to a Hackney with ability of passing on motion, they would/should have produced motion. Instead, only 1 that I'm aware of was ever bred and she produced a really nice foal crossed on a TB that got to be larger and think is aimed at Eventing (not sure since sold and I have no idea where she went). The pony that did get the sometimes extreme motion was the mare sired by an Arabian stallion out of the Hackney mare... And her resulting 1/2 Shetland filly is a bit more reactive and has decent motion (more what I call fancy rather than extreme) w/o getting the height - knee or hock. LOADS of extension.
You might check with some of the ASPR breeders - there is a page in The Journal with their ad. Also, there used to be a Hackney breeder that advertised thru the Recreational Equine Driving group in Yahoo. I'll see if I can drop some feelers for you, they might still have/know of Pinto Hackney lines...
I'd love to hear what you find - if you purchase.