Forced hot air and mini heat pump
It'll work well as long as your mini split unit isn't conditioning the area near the thermostat for the forced hot air unit. If they're too close together, the mini split will make the forced air thermostat think it's always the perfect temperature, so it will never call for heat, and the rest of your rooms will never be comfortable.

The added expense of adding a mini split to multiple units is probably going to be a lot more than having someone fix the problem of the forced air unit constantly turning off and on. Running the circulation fan for 35%-100% of the time in the heating season might be a good and much more inexpensive solution without looking into it further.