Catahoulas are amazing dogs. Mine is a blood trailer, hog Bayer, deer finder, rabbit protector, house guard dog, etc. But they have a long puppy stage and can be stubborn as hell. But I wouldn't trade mine for anything.
Blood trailing, that is an interesting thing. Same dog that I could free cast in deer country that would go find a masked bandit could be put on a long lead, sicced on a blood trail and would walk you right to a downed deer. Could track like a bloodhound, same thing with a broken trap chain, except you turn them loose when the track warms up and listen for them barking at a bayed coyote. The fact that they can't run an old track and stick it has nothing to do with nose, they can smell it, they just have no inclination to follow it unless you make them. It's about attention span. Downside to a jack of all trades dog is that it is easily distracted. Curs have a trait I call handle. Curs have too much handle to take a cold track very far without coming back to check on the master. Hounds have less handle. You are still a pack member, but you are expected to keep up, and function independently.
It has very little to do with training, these traits are genetic. They are either born with it or they are not. The main thing that needs training is the handler. Somewhere, on the American frontier, dogs that didn't have enough handle to learn which animals to leave alone came to an abrupt end, if they were to be hanging out on the cabin porch, rounding up stock, and hunting. This is the cur. Hounds were kept in kennels or tethers, some hung out loose at the big house, but somebody kept an eye on them. The traits that were needed were present, and culling focused traits based on need. Curs have herding dog traits, they have coursing traits, they have mastiff traits, they have hound traits, and there are a few bird dog traits. Probably because they are a mix of all these things more so than they have ancient lineage of Spanish herding dogs and Spanish war dogs, but who knows.
Here is a trait for you. Homing ability. It has all but disappeared from most dogs. You can still find it in some lines of hound. My grandfather decided to take his hunting dog to the place he traveled for work, during the WWII era. Dog got separated, didn't recognize it's surroundings so it went home, about 400 miles away, took it a month, his family sent him a letter telling him not to worry. I have one that I know can do it from 20 miles out. Once she drops in to homing mode it is actually almost impossible to catch herm she won't come near a human, a house, and will set at a road and wait until she doesn't hear a car and bust across it like a deer. She will go back to where she left a vehicle, and if somebody is not parked there, she is heading home. This is after she quits a track, which for her is after about 30 miles of running or eight hours of running, whichever comes first. If you approach a road crossing she will change course. You have to be within a couple hundred yards for voice recognition. She hears a vehicle, turns and you get out and holler, you see her bump across the road 400 yards down, and she resumes course. Irritating and amazing at the same time. Anti-theft mode kicks in at the same time as homing mode. She finally figured out that my truck horn was me, took a lot of honking at feeding time I'm sure my neighbors loved that. Theft was a big deal in the 1800s, a lot of your fox dogs are "shy" as a result, you can't lay a hand on them, but they will get in their master's truck, or their kennel. Some people would interpret these things as a dog that doesn't listen, but there are a lot more things at play.
Breeding selection has huge impact and can have for hundreds of years, but it doesn't take long to lose traits when you start crossing. A good trait that is a dominant trait is a very rare thing, often a cross is more likely to give you the worst of both sides. You can cross breed and add traits, but those recessives aren't going to pop until the second generation, and it will be the third before you can isolate them, probably the sixth generation before weeding out undesirable traits from your blend. If you don't live in a country where arbitrary euthanasia of companion animals could be considered a felony you will be fine. Otherwise you are going to be putting a lot of what could be menaces into pet homes.