The coop should be big enough but I'd add a run to go with it. I realize you are not going to keep them until they really mature, but you may find them a bit crowded in there. I don't think you need to go with the normal recommendation on this forum because your plan is a little different, but you should be able to add a 4' x 12' run or preferably larger fairly inexpensively.
I agree you will be disappointed with the size of a dual purpose rooster at 12 weeks. I never process mine before 15 weeks and those are not real big. I free range mine so I don't necessarily buy all their food, so letting them age is not a big deal for me. I think in your case the weight gain after 18 weeks is not real cost efficient so you might plan on processing between 15 to 18 weeks. They are still not going to be huge, but I think you'll be satisfied with what you get.
Now, your basic question. Will they fight? Yes, probably, some. They will start sorting out the dominance thing when they reach puberty. That could be as early as 12 weeks and probably will be by 15 weeks. They will do peckingn order earlier. If they are raised together it probably won't be too violent, but there is always the possibility some will fight to the death. This is another reason for some extra room. If they have some extra room they can run away instead of being cornered and have to fight. What would worry me more, and I don't worry about it much, is that one gets injured and bloody and the others turn into cannibals. You will probably be OK but there is always the possibility something could go wrong. Even with a flock of pure hens, there is the possibility that one could get injured in a pecking order fight. You'll probably see more fighting with roosters than you saw with your laying flock maturing, but not necessarily a whole lot more. But then you might. It purely depends on the personality of the individuals.
If it helps any, I have hatched and raised chickens with the flock, as many as 8 roosters in one brood, and have seldom seen much serious fighting. I have never had one get seriously injured. Mine free range so they have plenty of room (there is that extra room thing again) so they do have room to run away when they a start losing a fight.
Good luck. Sounds like a decent plan.