If you are going to be concerned with heat loss from the tank then surely you would use the batteries to charge up overnight and then heat the tank on a schedule to the lowest possible temperature just before needed (05:30am for a 6am shower) at ~40°c to 43°c, The lower the tank temperature the lower the heat loss from the tanks as it will take longer to dissipate. If you are happy with this and provided you can get another battery at a reasonable cost that totally makes sense.
Again adding in Waste Water Heat Recovery would likely cost around half the amount of the heat geek tank for the equipment (provided you can access the down pipe or under the shower/bath) and would reduce the volume of hot water needed so while not directly improving COP it would reduce usage.
It all depends on what you want to achieve and where you live. Do you want to be Top of the SCOPS, have the lowest running costs or be the greenest and lowest carbon house. While very similar these outcomes are likely to require three very different approaches and may all demand very different systems and priorities.
For southern England we usually have around 4 months where we do not need any heat so provided you heat your DHW in the middle of the day when it is hottest outside (so the heat pump has less work to do) you should get a good COP (but likely not as good as the heating) and as the surrounding environment is warm heat loss will be minimal, any solar panels will also offset the electricity costs (yes this will detract from your export fee but did you put them up to be a powerplant or to be green and use your own power?).
As matt has mentioned the heat meter from the L3 kit is sited within a meter of my DHW tank so the COP you see is what I am getting, however if your pipework is fully lagged and insulated I would be interested to know how large these significant heat losses are. Surely if the heat loss from an insulated pipe was that impactful then there would be more people installing an ASHP wall hung near the tank or moving the tank next to the heat pump and manufacturers would not have guidance allowing for 10m pipework runs. This would be quite simple to test and check but unfortunately I don’t want to put a heat meter outside on the back of the heat pump, especially when they are not particularly cheap and any comparison with other non MID meters would always introduce a bigger level of uncertainty due to the accuracy.