rocket mass heater for second floor -- moving that heat to hard-to-reach places

One of the pain points of a rocket mass heater is "how do I get heat up on the second floor/up in my apartment/..."?  

Well, what if you have your mass on the first floor and then use some copper piping like a radiator system, and run it up to the second floor?  And dump that heat in a bell/stratification chamber there instead of a radiator?  a chamber that's flat on top and so you can sit on it, sleep on it maybe, receive some radiant heat from it, etc., but isn't too heavy to break the bank/the floor?

Now of course you may think you have the boom squish possibility with water heated very hot in an enclosed pipe, but this water is not under the kind of pressure that a hot water system is--it is simply steam running through pipes.  No more dangerous than a standard-issue radiator heating system.  

The stratification chamber can be radiator-shaped below if it needs to be shedding more heat to be functional, I don't think it does but I don't know for sure how these work to ensure thermosiphoning.  

Thoughts?

OK, so someone did already suggest this and maybe build it (hoping for updates)

https://permies.com/t/192732/Plans-house-heating-solution-Rocket#2210643

Some things in the discussion got confusing--pipes spalling?  Hoping for some clarification from Thomas too.  I don't think the old-fashioned radiator systems would spall out.