I'm suggesting mixing, with progressively more Breeze pellets in your regular litter. Honestly, I think it has taken me 2.5 bags of Breeze pellets to do a good transition.
You've already mixed a few pellets of Breeze litter in, so the next step would be to go to about 1/3 Breeze pellets and 2/3 your old litter. Then, in a week or two, go to 1/2 and 1/2, then in another week or two go to 2/3 Breeze pellets and 1/3 old litter. At this point, hopefully, he'll be using The Breeze as much as he uses the mixed box, and you should be able to just remove the mixed box. The Breeze box works with a small amount of litter, so I'd also reduce volume of litter in your mixed box as you go.
It's important, I think, to keep a whole Breeze litter bag worth of litter in The Breeze during this transition. Like you, I started out with just the one bag of pellets and put a cup or two in my old litter. My cats didn't start using The Breeze until I put more litter in the Breeze; the amount it comes with works, and the system wouldn't work well with more litter, but you do need that much litter to make the cats willing to use it.
This isn't a terribly cheap process; Breeze pellets are designed to stay on top, so when they are mixed with your scoopable litter, you are going to be throwing them out (in urine clumps) much faster than they are designed to be thrown out. Your urine clumps will also be less clumpy, as you have more and more non-clumping pellets in the middle.
You'll have to decide if the slow, awkward transition is worth it.