Interesting read - like lots of us on here, I'm always working out ways to reduce our usage and make the most of off peak electricity prices. Like @Marvin we're all electric, with PV, ASHP and in our case batteries not an EV. Now we're in the new year, I'm just working out what we've used this year.
At one point in your analysis @SteamyTea, you say a 20% efficiency loss on batteries would be a best guess. This is one thing I was concerned after I'd installed our batteries. What I've noticed is that at low wattage the losses are higher. If this is the case, then there's probably a base loss due to the inverter being 'on' so to speak and then a %age of the actual wattage being delivered.
An example from this morning, with a house load of 323W the inverter was actually drawing 397W from the battery, so 19% - which is about your best guess. Later in the morning with the ASHP drawing power, the house load was 2953W and the inverter was using 3187W from the battery (2452) and PV (735W), so about 7%.
Unfortunately for all battery users the lowest loads will be the most common and higher loads more intermittent, so losses would be closer to the 20% than the 7%.
I'll have to try to dump data from the inverter to get more data points, for example when the batteries are being charged, either from the grid or from the PV etc.