Mine can charge the battery up at 3.7/8 and the PHEV 6.6 kWh at the same time, just over 10 kWh, it may be possible the inverter/batteries could charge at a higher rate, Kezo the man to ask.
Have you looked at Octopus Cosy it designed for heat pumps you have 2 charging period in the same day.
Unfortunately I have suffered a brain injury and occasionally I get confused and often say the wrong thing.