Your right, the 11kW electric heater is what's killing your electric bill. I don't think rigging up a VFD will pay out as much as a thermal blanket and some sort of solar heat. There are lots of DIY options for solar.
You can wash of the filter carts and reuse them.
I wouldn't run the pump / filter and heater when anyone is in the pool for fear of electric shock, these pools make no provision for bonding.