Or potentially even look into a high quality Nokota stallion. That way you would have a purebred (or as purebred as this type gets anyways xD) but you could easily improve the get by picking a stud that pairs well with your mare. I realize it might be a bit of work since they aren't many standing studs, but maybe you could work with a breeder to get your mare in foal if, indeed, she is a good example of her breed. The Nokota Horse Conservancy - Breeders List
# It sounds to me as if Nokotas have a presence of their own in the show world, so why take a chance of a very....interesting, foal, when you could get a purebred nokota with the ability to do all that you are wanting it to do?
After doing a little research I have found that a breed characteristic is that they tend to be quite angular, which is opposite of what a warmblood is. Warmbloods are built for finnesse and power, but are streamline and rounded typically. I keep trying to imagine a Nokota x WB cross but I really just can't fathom what one would look like.
Is your mare a National Park Traditional or a National Park Ranch? I'm assuming Ranch, since you mentioned a Quarter Horse type build?