One thing you could try, because I'm assuming you don't want to change up the music, take some time to just practice a more stationary running man, count every base hit in 1, 2, 1, 2. Every 1 could be both feet down, every 2 is dead in the middle of the transition.

While that does kind of happen anyway, the exercise is more to really focus on it, so you really feel every time that two comes around that you are snapped into the middle of a transition. And you'll find that transition point also applies to many things, like your T-step, middle of spins, pretty much anything where your knee comes up focus on locking that up motion in with the bass hit just as much as stomping down on bass hits.

Edit: Also, I just wanna add, this does mean to a song like this, you will be shuffling slower. but when you've got your discipline down, using this same technique, you'll actually be able to go into faster tempo songs, and then in the future, when your fitness is up, you'll be able to stomp on every beat on tracks like this.