Inductive loads are funky when it comes to generators. Inverters might be the same. Start up current for motors is roughly 3 times its rated run amperage. I once tried to run my washing machine with a 2500 watt generator, it wouldn't budge for the spin cycle.
Your 1000 watt DC - AC inverter doesn't mean you'll get the current you need. What is the DC voltage input? If it is 12 volts, at 1000 watts (look at the spec it might only be for a short period of time as it would read "peak") its maximum amperage would be 83 amps on the DC side, 8.3 amps on the AC aide. I don't see how using this inverter for power outages can work. A lead acid battery can provide that current but it would be short lived.
All of these DC to AC converters, even those that come with trucks and cars are for light loads such as computers, printers, lighting, etc. Not for power tools or motors.
You said keep it simple. Rent a generator and try it on your pump to see if it works. The big question is how do you want to handle power outages, automatic switch over or a manual start of a generator and using a transfer switch. Either way it can get expensive. You cannot go cheap since you do not want to burn out your pump motor and need to be safe. I've seen this type of question many times over the years and its always someone trying to use what they have on hand. Living in Florida we get our share of hurricanes and power disruptions so I understand the need.
