Hello Matt, Welcome to permies!
Not sure what your weather is like right now but for me, a rocket sauna sounds really nice in the middle of winter.
As far as being concerned about exhaust gasses leaking into the room, your safe since the draw from the fire will always be sucking air inwards under negative pressure and out the building.
Even small leaks in the system would only leak very briefly if you don't already have an established draft.
Of course, leaks are best filled in ASAP as they will rob the draft from the
feed tube which is where you want it.
I'm not sure what you mean by "balloon". Do you mean the gas cylinder acts like an enclosed area?
I am pretty certain that your chimney liner will not work as it just won't be able to withstand the high temperatures that rocket stoves get. Others have tried ceramic chimney liners in the past and they have cracked badly due to the immense thermal shock inside the combustion zone - particularly the heat riser. May I suggest instead you try using a product called
superwool.
To make a 5 minute riser out of it would fit your bill perfectly. See here to learn about how to make one:
Working with Morgan Superwool Plus ceramic blanket
You may find that the river rock shield all the way around your heat exchanger may rob too much quick heat from getting into the sauna. You may want to limit it just to the top or sides and have a certain percentage of the heat exchanger exposed.
One other place of concern is your angled feed tube. Unless your going to be there all the time to monitor how the
wood is being delivered to the fire, the angle itself prevents the wood from reliably dropping into the fire below as its being consumed. A J tube is a much more reliable way to ensure the wood drops as intended.