Am I being too picky for buying a new horse?

You're paying your hard-earned money for this horse, and if you want to be picky, then be picky! It might take awhile to find the perfect one, but to me it sounds like you're being really responsible. You're not going out and falling in love with every single one and impulse buying. And, you're having vet checks done. You've made your criteria, so stick to it! You will eventually find one; there are tons out there needing homes! I'm not sure if a seller would know if their horse is bison, turkey, coyote safe though..lol. Good luck with your search!