your issue got nothing to do with a back.up battery.
the height of your return pipe outlet, and the level of water above the return pipe outlet. the difference is the volume your sump need to hold.
example, if the return pipe outlet is made to be in the mid height of the tank, when powercuts, all the water above the outlet will backflow.
the water level in the tank should not be too high above the overflow clutter as well.
no offense, but, drilling holes will.make matter worst, it will be continuing feeding the back flow. the type of pump used doesn't matter at all, because during powercut, all pumps become dead pump.
the reason getting a back up battery is to focus on providing aeration and water circulation. the LS can last very long having these met. the backup motive is not meant to keep the entire system running.