I'm not really sure, since I don't know how irradiation chambers treat neutrons. I have to assume they absorb them, but no idea what %.If I can make it work, I'm thinking of building an 8-core as one boiler surrounded by fuel cores surrounded by boilers surrounded by reflectors, and no control rods, and then replace some components with irradiation chambers. Does anyone see a reason why a design like that should or should not work? Remember my main objective is not power, but the reactor should still generate some.
Assuming they absorb at 50%, I'd try your 8-core, 1 boiler design, surrounded by chambers, surrounded by reflectors.
If they absorb at 100%, the reflectors would be extraneous.
If your reactor gets too hot, I'd replace one or more chambers with boilers (which is basically your own plan already, in reverse, and more hazardous)