How about this as a complex setup.
Install a bypass damper on the furnace. Protects motor. Once the bypass damper is installed, the rest can be tried with cardboard.
Close off all of the return air ducts except the ones downstairs. Let fan run all day for the trial.
If it works, then install motorized dampers on the return ducts. A differential thermostat that looks at "basement temp" - "house temp". If it is positive by some amout and your on LP and there is a call for heat, then run fan and close all the return air grills but the ones downstairs. You may not even need the "if there is a call for heat". That just puts an upper limit on the temperature, but this stat could turn on/off the propane heater.