We have used induction cooking aboard boats for 3 years now. We have a Newwave, and a Duxtop induction burners.
We were able to run the cookers off the 1000 watt Honda. You can do most of your cooking on medium, and that uses in the 680 watt range or sometimes less, which is in the capabilities of the Honda EU1000.
With our C Dory 25, we have 200 amp hours of LIFEPO4 batteries, a Victron 2000 watt PSW inverter/80 amp charger. That does a great job with the induction burner. Several C Brats are using a much cheaper inverter. The Honda EU2200 does fine with both the induction burner and microwave (So does the inverter, but it is a huge draw even for the Li Fe PO4 batteries..)
Be sure you have the battery power for an inverter to run the induction burner. The inverter may draw up to 100 amps. In 30 minutes you would take a group 31 battery down to where it is 50% discharged (which is about as low as you should take it).
I have run inverters off 2 group 31 AGM batteries to run a microwave--the induction will use less power.