I keep telling everybody that the design of those ceiling speakers is absurd.
The best solution is a really good full range driver. This one is excellent value. It is the
Mark Audio CHN 110. It is well below your budget. The FR is excellent. I recommend you mount them in 0.25 cu.in back boxes for optimal performance and acoustic isolation. Fill the box with Polyfill.
I have four of them mounted like this.
With the white grill on the speakers are unobtrusive.
The results have been excellent. I maintain that is by far the best solution to ceiling Atmos speakers around, and it is highly cost effective. A good full range driver is ideal for Atmos ceiling speakers. I have had hem in for three years now, and the results are excellent. From an acoustic point of view that is a far better solution than those drivers with tweeter and mids stuck in front of the cone, which frankly is a very bad and stupid solution, and certainly not a quality or sensible audio engineering.