Hi, @2stacksterry, and welcome to the forum. Although you've asked one question, there are several others linked in here and a few assumptions you've made that could do with a bit of challenging or testing. As a result, my answer might not be quite as quick or clear cut as you might hope.

Firstly, some easy stuff. Your dishwasher and washing machine are likely already very efficient and so load shifting them, whilst an easy thing to do, will have a miniscule impact. The dryer is more important, but you're shifting it anyway so no worries. As for trying to load-shift other family activities, I'd strongly suggest you don't do it unless it's really easy to do; the whole point is that things fit round your family life, not the other way round.

Your calculations of 4000kWh per year for non EV/heating stuff equate to just under 11kWh per day which is pretty much in line with most of us. A daily consumption of around 10kWh per day is the normal rule of thumb used and mine tends to fluctuate between about 7kWh and 12kWh. In comparison, my daily averages for heat pump and EV are about 14.5 and 8.75 respectively. In your position, I'd up your heat pump estimate until you get a better one from a proper heat loss calculation.

Now for the slightly more involved stuff.

Trying to run a heat pump in a load-shifting way is not great on your wallet or health. In order to do what you're suggesting, you'd end up with a hot house during the night (and therefore quite probably have worse sleep as a result) and a house that gets too cold during the day to a point where it's at its coldest during the evening when you're most likely to want to relax somewhere cosy. It'll also mean your heat pump has to operate hard to bring the temperature back up again before turning off completely, and that's analagous to a boy racer accelerating hard as the traffic lights turn green only to get to the next red light quicker and have to come to a standstill again. Far better to operate the heat pump low and slow 24x7 or at most have a minor heat setback of a couple of degrees overnight. None of that fits in with the idea of shifting load to a cheap tariff time. I'll add further that most of your heat pump requirements are for the colder half of the year when your home will lose more heat and your heat pump will have to work harder with catching up on heat losses.

Havenwise, Homely and other similar services certainly have the potential for running your heat pump more efficiently but they are not a magic bullet. Most of their claimed savings are actually based around taking a good installation that's been configured badly and making it run low and slow with weather compensation, which you can do yourself anyway. They do have the potential for extra savings around time of use tariffs - and those savings may well exceed the cost of the service - but are not on the kind of scale to warrant your changing your tariff strategy overall. In short, I'd ignore them for your initial calculations and only start thinking of them as a tweak once you've got a system up and running already.

When you charge your EV is easy to choose, but time-shifting any other significant load is largely impractical unless you have a home battery. If you have to consume electricity during the peak periods (7-10am and 4-7pm for Agile), the last thing you want is to be buying your leccy at those times.

In your situation, I'd rejig your calculations assuming your heat pump is expending closer to 23-24kWh per day for half the year for heating and about 2.5-3 kWh per day for the whole year for DHW. I'd assume your heat pump needs to run constantly for heating and therefore cannot be significantly offset and I'd assume (unless you've several teenagers that feel the need to shower every day and use the whole tank in the process) all your DHW consumption CAN be offset.

As for tariffs, I would avoid Agile without a home battery to allow some time shifting. It's precisely because I have a battery that I can store charge to get me through the expensive periods and therefore bring my average import price down significantly that Agile makes sense for me. And in your situation with only the EV capable of being time-shifted, I'd say an EV-specific tariff is far more sensible.

Nonetheless, if you rehash your calculations as I suggested, you may find solar PV and/or battery may start to make financial sense instead. It still won't work for everyone - @jamespa is a good example - but for quite a few of us it does.