RIR are listed by Henderson as infrequently broody. I agree that a broody to raise chicks would be by far the best way. You could line up a source or two for chicks or fertile eggs in advance, then put them under her when she's been broody -- this can be for just a few days, or longer. IF one goes broody for you. You will know whether you have one that goes broody long before you need to start replacing them, though.
Without a broody, in your position, with no space to have them separate but seeing each other for a few months, and no space to add a coop, I would replace them all at once with baby chicks, and buy eggs for a while.
You could also try to buy "laying pullets" but there are so many pitfalls in this that personally I would not consider it. Again, personally, I would not incubate -- much less chance of getting an undesired roo when you buy chicks, even no chance when you get sex links, and I don't want to fool with an incubator anyway.
Without a broody, in your position, with no space to have them separate but seeing each other for a few months, and no space to add a coop, I would replace them all at once with baby chicks, and buy eggs for a while.
You could also try to buy "laying pullets" but there are so many pitfalls in this that personally I would not consider it. Again, personally, I would not incubate -- much less chance of getting an undesired roo when you buy chicks, even no chance when you get sex links, and I don't want to fool with an incubator anyway.
