It's not a very good idea to keep the food in the coop, Tally, as it may get contaminated as well as taking up space needed by the girls. Have you got a covered area within the run for the feeder? Take it in at night in case any vermin find it.
Hay does get very messy, doesn't it- you may find its better just to use shavings in the nestboxes, and shavings or newspaper on the floor of the coop, as either of these make it easier to clean out.
The smaller boxes in the rabbit hutch coop will be fine for the bantams, and one big box between two will do for the Brahmas, so long as they have the sense to use it of course. How big are the boxes in the proper hen coop? If you would prefer it if the bantams layed and roosted in one coop and the big girls in the other one, you could easily train them to do that. Just separate them into two adjacent flocks by stretching a length of netting across the run between the coops. The girls who are next to the rabbit hutch coop will naturally go in there, and you will need to watch and encourage the others to use the proper hen coop when dusk falls, maybe for a night or two.
So long as there's enough room and suitable nestboxes in just one coop for all of them, another idea would be to just use the one which is largest and shut the other one up. It's often very useful to have a spare coop, eg if a bird is sick or injured, or if you are introducing new hens and want to keep them separate at first, and if they were using both coops at once you couldn't do this. So long as all your birds are getting on well together despite the size difference, they will be OK in the same coop , and seem to have chosen this anyway from what you are saying.