I can't help with the dwarf gene. I've tried but can't get my head around the different genes and what the outcomes will be.
The dwarf gene is a recessive sex-liked gene. I have to think about it but I can eventually figure out who will give it to whom. But what are the practical outcomes of that? That can get confusing really fast.
I don't know if them being dwarf helps keep them alive so they can breed or if the benefit is that they eat less so they are cheaper to keep as breeding birds. If they are miniature Cornish X and grow as fast aren't they going to have the same health problems? To me, costing less to feed isn't a big deal at our scale, we don't keep that many. But if it makes it easier to keep then alive so they can breed, that would be huge.
You'd have to figure out how to keep it in the right birds in your breeding flock. Do you want it in your boys only? Your girls only? Would you need to keep a separate flock to manage that?
Would you be happy with a miniature CX. They would put on meat really fast but the final product would still be miniature. There are only two of us, I'd be OK with that but if you are feeding a family of seven, maybe not.
Are you crossing them with dual purpose chickens or trying to breed them to themselves? I could see breeding a dwarf CX hen to a dual purpose rooster. Since it is a recessive gene all the offspring will be "big". But how do you maintain that through the generations? Is that what you really want?
I'm sure I'm missing many implications of this. I always do. But it is a fascinating problem. Good luck.