You might be able to figure things out this week. How big is your sump basket? Is the pump kicking in now? Sit there for 15 minutes and count the number of times it cycles. That should give you a decent idea on how much water is coming in. Then figure out about how high the water has to go before it flows by gravity. The spec for the pump will say something like that it can pump 2,000 gph at 10 feet of lift. (the gph drops dramatically the higher it has to pump the water). The answer to your specifics will give you an idea of how big of a pump you need. If you match the size of the pump as close as possible to the amount of water your will face you can maximize the amount of time the battery backup will last.
Faced with this problem I took a standard boat sump pump and modified it so I could hook up a garden hose. The I took an old shop extension cord and wired the pump so I could hook it up to a car in the garage. So just prior to having Noah float by I could hook things up in the garage and be good to go for as long as I had gas in the car to pump up the battery. Now that I am adult I bought a generator and wired the house to take care of things.
Inevitably at least twice each season I will leave the house, drive 45 minutes and walk some of my favorite grouse spots for hours and hours, seeing nothing. Admitting defeat on that day, I will drive 45 minutes back home, only to find a covey of birds in the driveway...
Colonel E.H. Taylor Small Batch
Glenmorangie Highland Single Malt
Copperwing Distillery in St. Louis Park has a nice smooth whiskey. Supposed to introduce a new bourbon in a couple weeks too.