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That leaves us with a bit of peak electricity use running background stuff, like the sewage treatment plant, borehole pump, water treatment, cooking and whole house ventilation system and other appliances.

You obviously have a high level of energy optimisation and monitoring in your house, very impressed. Judging by the above you must be in a pretty "off grid" location too.
 
That's very good to know. When we first wanted to shift to Bulb they told us that smart meters wouldn't work on E7, and that they couldn't arrange a meter change to an E7 meter. This seemed odd, to me, as all smart meters have the necessary stuff included to operate any sort of off-peak tariff, even one with lots of different rates at different times of the day.

Bulb advised me to get our meter swapped to an E7 one with our (then) supplier, SSE, and once that had been registered, to call them back and switch over to Bulb (took about a month after the meter was installed for its number to appear on the database).
Bearing in mind that your ASHP will be at its lowest efficiency when your electricity is cheaper (in the night, when it’s usually colder), have you crunched the numbers to see whether the increased efficiency in the day time might offset the higher energy cost?
 
Bearing in mind that your ASHP will be at its lowest efficiency when your electricity is cheaper (in the night, when it’s usually colder), have you crunched the numbers to see whether the increased efficiency in the day time might offset the higher energy cost?

Makes an almost immeasurable difference. The amount of heat in the air is directly proportional to absolute temperature, so air at 10°C (283.15 K) contains only 3.66% more heat than air at 0°C (273.15 K).

Factors other than air temperature have a much greater impact on efficiency, and generally ours seems to average a COP of around 3.5, or a bit more.

The major factor that impacts efficiency seems to be humidity and temperature together. Humid conditions cause the ASHP evaporator to ice up, which then means that it runs defrost cycles in order to melt the ice. Every defrost cycle runs the ASHP in reverse (in cooling mode) and so pumps heat out of the house back into the evaporator (now a condenser) in order to warm it up and melt the ice.

Best efficiency seems to come with dry air, despite there being slightly more heat in humid air. This means that dry weather at around 5°C gives pretty near identical performance to dry air at -5°C in practice, just because there's almost no defrost cycling.