@susannasaunders

That's a serious amount of solar PV given the sqm of your house! You should be in a great position to run a heat pump of whatever flavour off of cheap electricity. That changes the equation somewhat on when to run A2A. You could conceivably run it much of the time, with the TRVs on the living room radiators stopping the GCH from heating that room. Put the thermostat for gas heating elsewhere and use a lower set point for that and the A2A could do most of the work, particularly if you effectively have the GCH off most of the night. There's definitely quite a few things that you can experiment with to get the right set up that works for you.

To avoid drafts, you can use the indoor quiet mode where the fan is barely audible and you just won't notice the airflow. The output is lower, but with the low heat loss of your house that is likely still enough to keep your living room warm. Perfera indoor units also have something called "Intelligent Eye" that detects if someone is in the room. With that feature turned on, after 20 mins of no one being there it will drop the set point by 2C to save energy, and automatically up it again when it sees someone return. It also avoids directing air at you to reduce drafts. Overnight, you can let the A2A run in auto mode, which adjusts the fan speed as necessary to reach the set point quickly. 

There are A2A systems that do hot water too. Daikin Multi+ is one, but they are bigger multi-split systems, for example 6.8kW capable of connecting to 3 indoor units.

One thing to realise with a semi-detached is that permitted development only allows for one heat pump (outdoor unit). So if you wanted A2A and A2W as separate outdoor units, then you would need planning permission. If they were sited appropriately and the noise calculations worked out fine, then there is no good reason why permission shouldn't be granted. Having to get planning permission is a PITA though that adds time and cost, and needs to be done prior to installation of the second heat pump.   

I suspect that the A2W and A2A BUS grants will be cut sometime in 2027, as the budget just took about £750 million off the overall funding for them and this financial year it looks like the total funding available (£400 million) will run out around the end of the calendar year (only £143 million left at the end of Sept, half way through the financial year). There's a whole thread here about A2W installs being expensive: https://renewableheatinghub.co.uk/forums/renewable-heating-air-source-heap-pumps-ashps/why-are-ashp-installs-so-expensive/

The swings in temperature with your gas CH are likely down to the flow temperature being higher than needed for the low heat loss of your house. This means once the thermostat switches the heating off, the room temperature tends to overshoot due to all that (too) hot water in the radiators. You can turn the flow temperature down on the boiler to alleviate this problem. You can probably run at a flow temperature of no more than about 60C (50C right now before it gets near 0C) and that would make the boiler more efficient as it would enable it to operate in condensing mode. Better still you could get weather compensation fitted to the boiler, so that it reduces the flow temperature when it is mild outside. We have this on our boiler and at present for the short times that the gas CH comes on the radiators sit at about 35-40C. This leads to very stable room temperatures and low and slow heating exactly like an A2W heat pump would do.