Be careful with that countertop induction burner. 'Careful' in the sense that if you don't pre-heat pans before you go to full-on, it's easy to warp the pan - and a warped pan doesn’t work as well on induction.

Given that electricity is unreliable, why not look for a camp stove that fits directly on top of your electric-burner stove? These are essentially a cooktop in a box that you can either attach legs to or put on something. Dunno about the propane costs where you are, but it sounds like electricity is expensive — so it might be cost competitive. And you can cook during a blackout. For safety, you want a setup with the regulator at the tank limiting the pressure in the hose. If butane’s available, and cheaper than propane, choose that. We can’t use it here in New England because it gets cold enough that butane won’t vaporize.