I am sure you are but as a suggestion, I would carefully consider the inhabitants of the predator tank and the reef tank if you run them together. The size of some of the predator fish, their food input, and the waste produced may limit your coral options if you run them all in series. 240 gallons with large fish, sharks, rays, will require more skimming, carbon, GFO, etc. if you want your 120 an SPS tank. I have never done a combination like that but I would seek out others that have if you have not already.
It would be simpler in my view to make the large tank fish only but smaller species and more conventional in order to minimize phosphates and nitrates. The food fed to the fish is the major source of phosphate input as Randy Farley and others have written over the years. Larger fish need more obviously and that will likely require you to choose simpler more nutrient tolerant corals or go with a much larger skimmer. The larger 240 might overwhelm the 120 with nutrients. That maybe fine as long as your equipment can handle the higher load.
I have seen systems with SPS tanks and fish only tanks work, but the fish were large angels, tangs, etc.
Certainly you could run the predator tank on it's own circulation/filtration and that would take care of the nutrient issue. Or you could simplify the reef system. It might take some empirical trial and error.
But in any event good luck, I hope it continues well you have an interesting project.