You still haven't explained why your load is unique to all other HVAC loads.
Why is it so important that the system perfectly match the heat gain 24-7-365. Inverter units do an incredible job modulating to achieve capacity control. However at a certain point the most efficient and effective thing to do is simply cycle the unit on and off.
What is so special about your setup that that's not an option?
The 1kW min load is a night-time scenario and so the units would need to meet this 8hrs*7 nights or 35% the time.
The concern about cycling is not only higher power consumption but also the potential blast of cold air every 15-30mins which will probably be notable even with inverter internal units.