Standard Cornish, (not Cornish X meat birds) light Brahmas, Australorps, Cochins, Old English game, Dorkings, Aracaunas, and a lot of the bantams tend to be very broody. You need a breed not bred for high egg production, they tend to have broodiness bred out almost completely. You can keep your RIR's and add a couple of the broody types, and stick any eggs you want under them, when they go broody.
Put a bunch (4 or 5) fake eggs, golfballs or some such, in a nest when you get some of the broody types, and then wait. When one gets broody, she'll latch on to that nest, and won't want to get off of it. Then you can take out the fake eggs, mark the eggs you want her to hatch, and put them under her. Mark them, so when other hens add more eggs you'll know which they are and can remove them. Or move her to an isolated area where the others will leave her alone.