Proper draft is key to the whole operation. For example, a properly functioning
rocket mass heater even when there is no fire will often have a natural draft that you can test with a small flame or an incence stick over the
feed tube. This test
should prove to you that exhaust can travel downwards before exiting again vertically.
The one big difference between a
rocket stove being the engine of a rocket mass heater vs a regular
wood stove is a much hotter fire and cleaner combustion. There would be a lot of creosote and
ash buildup in that bell with the cast iron stove in there which would not be good or safe at all. Kind of like putting a VW beetle engine in a ferrari.
There have been others that have modified a conventional stove to make a batch box heater which I think is about as close as your going to get to implement your idea.
Hope this helps!
Batch Box using fisher stove
Batch Box using Jotul stove