I know you probably don't need this anymore, since it has been almost a year. I do have a solution though, and you were insanely close to an optimal system.

I have done the same thing as you, where a part divides in 8, 4, or 2 and follows the exact procedure. The most effective optimization you can do is encapsulation checking. if the part you want to divide is entirely contained within the intersection part, just delete it from existence instead. It's also key to structure your connections properly when you make a system like this, I have my setup staged like (PreSim > PostSim > Heartbeat) so you aren't wasting frame time

I will also say you should only make a percentage of the divided parts act as debris and only render them on the client side to save on server performance.

Here is the DevForum post for my implementation: Roblox DevForum - Shatterbox | Voxel destruction made simple and optimized