Hello all, this is my first post at BPL!
I had some thoughts on regulating the thermal feedback to the inlet tube based on temperature. Don't discard your heat shunt concept just yet.
You might be able to achieve regulation (preferably automatic regulation) by either varying the thermal conductivity of some parts of the stove, or by varying the exposure to thermal energy of some parts.
To vary the thermal conductivity of the structure, it would be nice to have a material that has a thermal conductivity with a strong and inverse dependence on temperature. As the temperature of the conducting parts rose, the conductivity would decrease, thereby reducing the thermal energy transmitted to the fuel. Unfortunately, I don't know of any such materials.
But, varying the exposure of the inlet tube and connected parts may be possible. In this case, you would want something to move as the temperature rose. What I imagine here is one of your flat metal shunts made out of bi-metal sheet. As the temperature of the shunt rose, the shunt would bend away from the flame, reducing its exposure and consequently the amount of heat conducted down to the inlet tube. The regulation would vary smoothly with temperature. Alternatively, you might find a shape memory alloy that would bend out of the way at an appropriate temperature. This deflection could potentially be much greater than with the bimetal, but all the deflection would occur over a narrow temperature range, which might be ok or even desirable. Or, you could go low-tech and just put your shunt on a hinge and manually flip it out of the way or adjust it once the stove is warmed up, at least for initial testing. You would probably want the rest of the stove to be designed to contribute relatively little heat transfer to the inlet tube, so that the moving component could have maximum control of thermal feedback.
You might think of other variations on this theme.