Thank you for taking the time to research and elaborate. I went down the rabbit hole of reading all about cold nosed and hot nosed dogs last night as well. Fascinating. It sounds a little bit similar to differences between air scenting dogs and mantrailing dogs in search and rescue, just in a different context.
From my experience, almost all dogs can distinguish -or learn to distinguish- between old and fresh trails, most can learn to follow a specific scent (trail/track), and most can learn to air scent the target odor. It does take a special dog to successfully work a very old trail though! But in general, left to their own devices, most dogs will also naturally switch between following the ground scent (track/trail) and air scenting, like your Catahoula- but yes, of course some breeds and individuals can have a strong preference towards one or the other. You can really see that in mantrailing (my biggest passion), where you allow and encourage each dog to work as naturally as possible to get the job done. Sounds like this is what hunters discussing advantages of “cold and hot” noses in online forums are trying to do - find the dog with the most compatible natural style, that works best for them personally.
When it comes to recall and preventing wildlife chasing, I don’t want to add more fuel to the fire, but I think people tend to underestimate the power of an excellent, really well trained recall, paired with a strong bond between dog and handler. In my circles, good hunting dogs are absolutely expected (and considered capable) to be able to control their impulses and have reliable recalls completely “naked”, including scenthounds. They were bred to be independent thinkers, but not to be unruly - they were also bred to understand how to be a team with a human.
But I don’t want to moralize. I used to be in a similar situation with a young, super high prey drive dog that desperately needed off leash time for his own sanity as well as mine. I understand the worry and frustration. I decided to go the recall training route and got so, so much out of it.
I wonder if you might enjoy some structured scent work with your young rascal? Working on something as a team is so cool, and dogs’ noses in action are absolutely amazing.