Overgrowth is your problem. Rics and yumas are hotter than discosomas as I understand...not too much of a problem until one of two things happens: the lps grows, or the ric multiplies and gets closer to the lps.
If I were doing such a tank, I'd a] yes, run carbon: just keeps the chemical wars at a minimum. b) make sure no lps sweeper tentacles can reach a mushroom [they go where water flow takes them] c) keep the mushrooms on their own rocks and try to create some sort of barrier, like a gap in the rockwork, that keeps 'islands' or 'mesas' of rics or yumas permanently isolated, to keep conflicts from happening.
LPS with short tentacles: frogspawn and hammer [compatible with each other: can touch and mingle]. Fox. Candy cane [caulestra.] Hot: torch coral, same family as frog and hammer, but not to be put touching anything. LPS with 6" sweepers: bubble, tooth, galaxea, maze brain. Sweepers come out at night, or during feeding.
For the rest, it's just going to take clever rockwork and some monitoring, but you're right, that the rics and yumas are slower in reproducing. They'll spit chemicals if annoyed [you'll see several mushrooms contract and stay mad for hours] but the carbon will get that out in fairly short order. Unfortunately carbon removes some good stuff, too, and I don't like to run it non stop---you can judge your own tank's behavior and see if you dare take it out.
The only other difficulty, and not a large one, for optimum growth, is that most of the lps are from the Pacific, and rics and yumas hail from the Caribbean, but the difference in chemistry ought to be fairly minor.
LPS like moderate light including mh, but need to be acclimated to really strong light, raising them a bit per week. I have an insanely growing hammer that's 18" below a 250 mh, 9" below the surface of the water.