One thing is for certain, you will need more batteries than you want to use IF you want to use a heat pump and solar only. The compressor needs a regulated voltage and it must stay within that voltage and , they are almost all AC that can heat a house anyway so an inverter is necessary. The compressor has to be able to get the current it needs whenever it needs to operate and panels by themselves cannot guarantee the supply of current, moment by moment.
If you can get the house heat loss down to 2-3kw, you might just be able to make it work (with batteries and inverter), and you use solar hot water too.
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