I have all of the above and I monitor it using Home assistant so my system can make intelligent decisions on energy use. Below is a summary of my thoughts and findings in no particular order:-
Thanks John - useful to others.
We are fairly ahead of the game already, but I'm always considering adding to our existing system.
1) Heatpump is unlikely to save you money, when the cost of electricity is high it just cannot compete with gas. For example today my gas price is 6.2p kWh, if I factor in boiler efficiency of 90% the true cost of heat in my home from gas is 6.89p. The heatpump has a COP of 2.5 to 4.2 or thereabouts dependent on model, outside air temp and flow temp required. Suffice to say mine runs at about 2.8 when the outside air temp is below 10 deg C. So with peak rate energy cost of 29.8p using the COP of 2.8 each KWh in my home costs 10.65p almost double what gas would cost. This cost can of course be mitigated by solar and batteries but running a heatpump from batteries has to be done carefully, the eat through kWh.
Our Air-Water heat pump averaged 4.75 COP over the winter and I would have thought our 35 y/o basic gas boiler would have been 80% efficient at best.
It seemed to drop down to 3.6 on the coldest days, but was high 4's most of the time. That is around 1/6th of the gas usage.
Any extra solar and battery usage for heat pump heating is going to be cheaper than the peak-time grid prices, making the heat pump much cheaper to run largely because it uses so much less energy.
2) A better way IMHO is to use air to air air conditioning units, they still have similar COP ratings BUT you're only heating the rooms you need, they respond very quick and you get the benefit of cooling in summer.
A good option for those for whom the wet-system replacement is difficult.
Downside is that it doesn't do hot water.
3) Batteries are a great way to reduce energy costs, my average electricity cost currently is 3.49p kWh due to charging from Intelligent Octopus GO, I export all of the solar I generate.
Indeed, if there is a surplus of solar power the cost of using the electricity is then the export rate.
I have the best of all worlds in my setup and the way it tends to run is when it's really cold and there's no sun (little solar) the gas boiler will run to heat the house.
Very clever!
Having a DIY/hybrid system does mean you can't get the grant, though, as you note.
It's an interesting situation to research and plan, youre certainly ahead of the game starting now, good luck and do keep us posted.
We've already got heat pump, solar and a single large battery (9.5kWh so ok but not as much as some).
However our solar is East and West facing so great in the Summer but terrible from mid-Nov to mid-Feb, which is exactly when the heating is most needed.
A bit more panel-age and battery capacity would be very useful for those cold but sunny winter days.
The problem for us is that we would need a second consumer unit in the garage and some rewiring to add another solar inverter. All the electrical works add significantly to the cost and that means it is not good economically (though it would be good environmentally) unless energy prices go very high.