80 degrees and 130 degrees are not that far apart.
you can just make the RMH and put an oven on top of the barrel. if you insulate it well and have a good thick layer of thermal mass you should be able to get and hold what ever temp you need. until you build an RMH to spec i think that modifying one is not very good idea.
in your drawing you reduce the size of ducting and run it under the oven. this wont work well what you want to do is enlarge the size of ducting and add fins to absorb the heat till you are at the CSA of the burn unit. lot of math but shouldn't be to bad. I would use copper as the heat sink fins and plate probably with a good granite or soap stone floor to the oven. 4 in of mass with 4 in of insulation then an outer coat (probably a lime plaster) make sure the copper plate is in direct contact with the floor of the oven because copper conducts very well but does not radiate worth beans.
Need more info?
Ernie and Erica
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I would guess that it's going to take some fiddling to get everything just right, but that is an extremely excellent plan and I do hope you'll share your progress. other than that, I don't have anything to add to Ernie's advice.
I actually see nothing tricky about the original sketch (assuming it is schematic and not intended to be precisely to scale).
With recent years' developments in thermal exchange and storage methods, I would suggest an improvement on the winding duct which will make parts of the floor hotter than others.
I would make a wide flat bell under the oven floor, much like the Roman hypocaust: a masonry floor supported on regularly spaced piers so that the warmest air can freely spread over the top of the whole space, and as it cools, it will drop and reach the exit at the bottom of the bell space. It would obviously take experience to be able to regulate the temperature as desired over time, but it should be achievable and repeatable.