I'd like to find a way to have my array work when I need it most!
You'll need to invest in a home battery bank. These batteries are built to simulate grid-like conditions by providing a constant stream of power to your house (until exhausted of course).
The power produced by the inverters would fluctuate too much for most electronics to operate correctly - as others have commented. For example, fluctuations from both the generation-side (a cloud passing overhead causing a drop in voltage) and use (the fridge or freezer attempting to kick on and drawing too much power).