For one pits cant handle the heat or a long race like a good cur dog
This is probably the greatest misconception that's been propagated over and over on hunting boards. Historically speaking, the APBT was selectively bred for over 200 years for combat and is largely considered to be the ultimate canine athlete. If the above is your general experience with a "pit" then you haven't seen a real APBT (today known as a gamebred APBT)...just counterfeits. In properly conditioned animals...you should not see any difference in an APBT and a cur as far as wind/heat tolerance goes.
The ones have owned/own will hunt on their own, if allowed, and have a decent nose...same goes for the majority of my ABs.