How sturdy is the floor around the stone enclosure? Could you add posts under the floor without interfering with basement use? A cob bench spreads the load out enough that a sturdy floor can generally support it. A cob/masonry bell concentrates the load enough that it needs its own foundation.
If you do want a radiator barrel for instant heat, that can probably go on the floor next to the stone box (with appropriate air space and insulation.) Then you can make whatever bench arrangement you like, ending with the stone box as the final bell before going up the chimney. There are airflow and other details we can advise you on if you want to go that route.
With the stone box opening 51" high and wide, you could actually recess a low bench partly into the opening for a cozy seat for two, as long as neither of you is extremely tall
Then you could extend a bench to one side for more seating in the open. It looks like the hearth extends 25" in front of the stone box so a bench could easily be supported on it.
You mention wanting to integrate with your state-of-the-art hydronic radiator system; I think the safest way to do that would be to incorporate in the bell a 10 gallon or more water tank at atmospheric pressure, with float valve for makeup to keep it full, and run a coil from the hydronic supply (before the furnace) through the tank to pick up heat. Then route the pipe back to your furnace so it can come on if the RMH tank is not providing enough heat. With your individual radiator thermostats, the part of the house warmed by the RMH will not call for radiator heat, and remote rooms can be hydronically heated.