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Have you tried going down the passive route...

Lots of exterior insulation around the building, triple glazing (this should reduce heating to near zero), natural ventilation during swing seasons and rather than VRF a radiant system. I understand that humidity might be an issue, less so for residential so perhaps a mechanical ventilation system in the summer with heat exchanger (more important really for the winter) and some dehumidification. This is what I see for extremely well performing buildings in Germany (building built today climate zone 5a). They tend to hook up to the district heating system so have the advantage of thermal hot water delivered to the building but maybe a really good heat pump will do the job instead if you have to all electric. Also have you tried solar thermal?

Those would be my first thoughts, something to ponder if you haven't already.

Annie