They claiming it would cover 75% of your usage sounds on the high side, unless they have some sort of yearly netmetering? I would check how they came to that conclusion before signing anything and get it on writing for future reference.
We're pretty diligent on our consumption. On April we exported 377KW and imported 160KW from the grid. The array produced 632KW. Its sized 7KW with a 3.6KW inverter, East/West facing. So as you see we only managed to use about 1/3 of the array capacity, with the rest being night usage, which includes mild heating this time of the year, mostly through the day and couple hours after sunset.
We have all all electric house, from water heating through cooking and climate control.
What I think would be a rational decision for you to consider is a zero export inverter, with or without battery storage. Those, only inject enough to cover your usage without any export. Any excess is stored on the batteries if available. Since you're not exporting you should not need permissions from the utility and in case you go with battery storage you can ofset any excess production during the night.
You tipically loose the ability to sell the surplus to the grid. But the price per MW here is just under £60, so I would be lucky to recoup £100 a year from that. I immagine the same is true in other parts of the world.
Same for battery storage.
For a 7KW system you're probably looking at a 10KW battery, but really run the numbers based on battery cost and install price. Assuming 20c/KW, a 5KW pack discharged 2KW every day would save you $730 over the course of 5 years, assuming the utility buys none of your unused energy back. For 10KW maybe you can tripple that, but those prices are a far cry from what you're paying upfront for the battery in the first place, unless there is a big spike in energy prices, you can keep the system running for many years past the warranty finishing or your electricity is significantly more expensive that the numbers I run above.
With the solar panels alone, maybe you can halve your electricity bill if you're diligent using loads during the day and waiting for good weather to run heavy loads such as laundry, etc.
Shop arround how much it would cost you to run maybe 5KW of panels with a zero export and see if that makes any sense versus what you are being quoted now. The installer should be able to advise about any required permissions.