FWIW, I just got a meter installed this fall that appears all but identical to your service meter. Mine is not a NET meter, but the same otherwise. Mine has 3 or 4 little bars at the bottom left that mimic the movement of the old spinning disc. They move left to right, then annoyingly disappear for a while before starting at the left again as power is consumed. It's not as easy to judge load as the good old disc, but still possible. You might check to see if yours has them too. Worst case, there's patience combined with the KWH counter.
When you say that your HWH has a "heat pump" mode, that makes me think that it's at least part of the issue. I'm almost certain that it's going to be able to run the backup resistance elements in "energy saver" mode. Plus, the fact that you know it's only good for a 10 minute shower leads me to think that you're pushing it near its limits often enough to know that. Unless it's in heat pump only mode it's going to kick the resistance elements on long before (and after) it gets to cold shower temps. See if you can live with "heat pump" (only) mode. If nothing else, it'll give you a clue about how much past the heat pump capacity you're currently going. Strangely, turning up the temp could also help in energy saver mode if it keeps the water hot enough in your normal use to avoid having the resistance elements kick on (if that helps, it won't really matter if it's in heat pump or energy saver mode - it's effectively just heat pump mode with a higher temp setting). And, while the thought alone is depressing, maybe you need a low (at least lower) flow shower head?? They make a difference. Adjustable flow heads are a good compromise between depression and hedonism.
When you say that your HWH is in the basement, but with no heat there, that really isn't going to make a difference. Think of the whole space inside the home as one sealed space (at least for this purpose). You can't take any heat from any space anywhere inside your home without affecting the total heat in your home. If you lower the total, you're going to have to make that up. It's more efficient to make it up with a heat pump than other methods (usually), but it's still going to cost you somehow.
You got me thinking, so I pulled out my power bill for a little comparison. I have a 3.500 - 4,000 sq ft home in a very cold climate. It's just my wife and I, but we work from home, so we're always here, computers and tvs are on a lot. What I think is interesting about the comparison is that I have almost nothing that uses electricity specifically to produce heat. We have all the normal electronic gizmos, and a fridge and a freezer in the garage big enough that Jimmy Hoffa could be in the bottom of it and I wouldn't know. That's in addition to the biggest semi-normal fridge/freezer my wife could find, in the kitchen. All are 8-15 years old. We don't have a well pump, or anything else to add noise to the electric bill. The only thing that is a problem is I do have my roof ringed with roof cables, which I use as sparingly as possible, and they can really suck up the juice when I have to use them. But I'm able to correct for that use pretty well. Hot water comes from wood, except for a short time in the summer when it's propane.
Looking at my bill, it ranges from about 300-350 kwh in the June to Aug ust area, to 400-500 kwh in Jan or Feb. Around 40% higher in winter. The need for some extra roof cable use in the warmer months of Oct. or March and April, can kick it to almost 500 too, but that's just wasted heat outside the house. I just plugged my wood furnace into the Kill a Watt, and it's 265 watts for the blower and HWH pump. If that's running 100% of the time, as it can get close to doing in the dead of winter, that's about the entire 200 kwh increase. There might be some slight need for roof heat, and a little engine heater use, but my garage fridge and freezers go into a coma to the point where I have to rotate warm water jugs into the fridge daily to keep it from becoming a freezer too. So, it probably somewhat balances out.
The point of all of this is that my bill bumps 40% ish in the winter, and while the heat from that ends up in my house, I don't have the bill bump from using electricity as a significant heat source. For the heat part, I'm burning around 7 cords of wood, very efficiently, and maybe 50 gallons of propane in the range which, being unvented, is also very efficient. I'm probably in a much colder climate than you, but keep in mind that my target house temp is 60 degrees +-3, - upstairs. I'll let someone else convert my wood and propane to KWH, as I'm sure somebody here has the conversion at hand. If you knew how many KWH hour equivalents of pellets and oil you're burning, that would be an interesting comparison as well.
Depending on how much pellet and oil fuel you're using, it might not be unreasonable for your electric use to triple in the winter. You're actually getting heat from your usage. I spend the short summer cutting wood. I don't have a mini-split (yet), but I'm guessing it puts out much more heat than a simple space heater, and I know that if I were to run a space heater a couple of hours a day, it would definitely help with my heat load. You've cut down the electric draw by cutting down the mini-splits, while probably increasing the electric draw from the pellet stove, and the oil burner, yet all the while burning oil and pellets you're also going to have to pay for.
First, you need to make sure you don't have something subtle or strange that's derailing you. There's a ton of ideas in the previous posts. You don't really need an "app" for that. The service meter is the ultimate arbitrator that your utility is billing you from. Weather it is easy to watch with an easily observed disc, or difficult because it only reads KWH, you can get the same data, it just might take more time and patience. Watch the meter, and flip the breakers, or install an electronic alternative, it's your time and money and up to you.
If you don't find a big problem, and even if you do, you should do some calculations yourself. I will suggest that maybe you're doing it wrong (no disrespect - it takes time to figure out this complicated stuff). Cutting the mini-splits at the expense of running the pellet and oil burners may be the wrong approach, depending on the cost of electricity, fuel, and the COP of the mini-splits at the temperatures you're experiencing. You need to figure out the break-even points between the heating options you have. With a COP of say, 3.0 and an equivalent cost of 1.5x electricity vs. (fuel cost + electricity use on the fuel burner), it should cost half as much to run the mini splits. COP varies by temperature though, so if it's a 50 degree afternoon, it's an easy bet you're way ahead with the mini-splits running. You should probably even run them to a few degrees above your desired temp to bank heat for the colder night (similar to turning up the HWH to save $). If it's -25, well, you'll know for sure if you've done the math, but there's a good chance you're ahead with a fuel burning device. If you calc it out, you'll know when it's time to switch from one source to another, or generally seasonally if you prefer not to make a profession out of heating your house. This site can also be a huge resource in helping you to improve efficiency.
In the end, the sad truth, I think, is going to be, that energy ain't free, in fact, it's pretty expensive, yet maybe in the perceived moment, cheaper than it should be. If you want the big house, the fast car, or generally, the carefree - I'll consume it if I feel like it - lifestyle, you're going to have to pay for it. The opposite of that is the mindful, conserve it where you can, and where it doesn't hurt too much, approach. You will probably find the ultimate solution in turning down the thermostat, taking non-orgasmic showers, turning off the lights when you're not absolutely using the light, killing the vampire loads, putting easily available wood into the woodstove, and choosing the right heat source for the job to be done at the time - those kind of things.
Don't take this wrong - yes, I exaggerate, but you get the point, it's a lot of small efforts, as long as they are not offset by a few big mistakes. You're getting monthly electricity from your solar panels equivalent to what I just paid $62 for. I know people who have $400+ monthly electric bills, and they're not in all-electric homes. They have more "spare time", but have less financial security, or have to work harder to make money. If you want to live the same life as my friends, you're effectively going to have to come up with the extra $338 a month. How you do it is your choice. Or, do this work, and have the small bill, and maybe retire earlier or better, or at least more securely.
I think you're trying have the small bill, that's why you're here, and I commend that. It's worth it, and doable, but if it was easy, it would be more popular. So far, I have a house that has room for my business, in a very cold place where I spend zero for A/C, and average of $40 a month for electricity, and every 5 years or so, I buy a few hundred gallons of propane when it's around $1 a gallon. That's savings i can put to much better use. And, I cut a fair bit of wood, which starts out free, though it doesn't end quite that way, yet it keeps me in shape, and beats the hell out of a real job.
Keep at it and you'll figure it out!
List could go on.
