How do you get your horse to go from an extended jog down to a regular jog?
I use my blocking seat - The same one I use to halt/stop, but to a lesser extent. ANY slwing down of pace on my show horse is done via my blockign seat - I don't do western but I have a few champion pleasure ribbons - A class where you must ride with draped reins, one handed, but in a snaffle. I have less influence like that than I would have if I switched the snaffle for a curb - I can do all manouvres with a draped rein in a snaffle that I can with my usual contact. My leg always means either forward or lateral - My seat can mean forward, maintain, OR stop/slow.
How do you remind your horse to stay collected, lift his back, and engage his hocks as he goes along?
This I use my leg for - I ask for forward using my leg and block the actual forward movement with a slight block in my reins (not pulling - Just not giving) and just enough of a block in my seat that his forward energy moves up and into the bridle instead of being translated into speed or tempo.
I do understand that you don't literally spur your horse to stop - I was just using the name. I also (though it may appear, lol) don't really mind how you train your horse; If it's working well for you, fantastic! Who am I to try and change the way you do things? I guess I am just trying to figure out the why - When the association apparently disapproves and the results are achievable without it, what your reasons are to continue to train it? Not snarky, genuinly curious. I am still curious as to which disciplines use a similar method - I will be the first to admit I have never ridden and only seen via video any western events, so my knowledge is limited to what I learn here!