How have you calculated that you used around 900kWh/year from those 4x250W panels ? That seems similar to what is possible in case of grid connected where all PV energy is used and not realistic offgrid usage.
I used to only have a 3x 240W PV array and was able to use 50 to 60kWh/month that is around 600 to 700kWh/year but I was utilizing the system fairly well with a lot of the energy used during the day for electric cooking.
A fully offgrid system will be designed for worst month. If space for PV array is not a limit then you should add as much as you can up to 0.9 of battery capacity so say you go with a 20kWh battery then you can install at 18kW PV array and only part of the panels will charge the battery depending on the amount of sun and you can use the excess directly for heating.
I fully heat my house using PV electricity directly and I do not need any cooling in summer as house is well designed and I'm in Canada Saskatchewan.
You are likely in a warmer place if a ground heat pump is used and that is just way to expensive in terms of cost amortisation it will never be a cost effective option.
To get some idea about the costs amortisation for a fully offgrid installation here are the numbers
PV panels have a cost amortisation as low as $0.02/kWh while best case LiFePO4 will have a cost amortisation an order of magnitude higher around $0.2/kWh. This is just the cost amortisation for this components there are inverters and other equipment that will add to the total cost.