It’s a shame you have no evidence about the insulated ceiling.
I have set the (3rd party) internal thermostat to 30°C, so that it continually calls for heat. All the balancing is done with the weather compensation. The weather compensation “curve” calls for water at 21°C if the outside temperature is 21°C or more, effectively switching the system off. Until then the system modulates down as far as it is capable, effectively reducing compression. Between times the system switches off.
As you mention, there is also demand for hot water. The water is on a schedule so adds demand to the system twice a day, mainly overnight and with 90 minutes starting 15:00, to top up the hot water ready for the children to get home and shower after school. The higher temperature demanded for hot water means that modulation is unlikely and therefore COP is also lower.
I have had solar thermal since 2006, so the heat pump hasn’t come on every occasion that hot water was needed and will not come on at all over the summer.