I've the option of setting my ASHP to produce DHW using a timer, and that's nice and simple.. But ever the burning desire to make things more complicated, suppose I could intelligently control it with a raspberry pi or similar, what algorithm would make an improvement over the timer approach? For example, I could download the weather forecast and get temperature and humidity readings projected and actual, and if the day was shaping up like the forecast, call for DHW at the warmest/driest part of the day.. ? I could avoid parts of the day likely to cause the pump to go into defrost, but what would those day parts look like? High humidity? Ambient temp of around 4 degrees? I'm not sure on the variables..

And would it make an appreciable performance difference over the course of a year? Enough to recoup financial outlay on components for example..

And further, suppose my house has two electricity supplies, one of which could be Economy 7/10, and suppose I had a way of alternating which supply powered the ASHP: the normal 15p/kwh energy tariff or the 5p/25p Economy7 one - are there financial gains to be had in using Economy7 and an ASHP for DHW? I suppose there must be, logically, if one can choose to use Eco7 electricity during the operational hours and "normal" electricity at other times..

Good project.
Working backwards first.

Having the ASHP wired into the normal side of the meter will give you the E7 price during the night.
Depending on your ASHP size and your store size (and insulation levels) you could aim to run the system at a relatively low temperature to avoid frosting, then boost for the last hour (or so) with a resistance heater.
I think I pay about 8p/18p on my E7 tariff.

Recouping all the additional costs is a hard one. I use about £130 worth of night rate to heat my water a year.
A friend of mine, who has a gas combi, uses less water than I do as she only showers (I like a bath). The reason I mention this is that down here, the cost of the water is greater than the cost of the energy to heat it. So she will be using a lot less kWh than I am.
So work out your DHW usage to see if there is a genuine saving to be made.

Finally you are dealing with weather, and specifically your own micro-climate. You could down load a few years worth of temp and RH data, calculate the dew point and AH and then, if you know the air flow and temperature drop though your ASHP, work out the frost risk and performance drop.
You may find that 50g of water freezing on the fins does not affect the performance that much.