> Their batteries only last a few minutes,
Today. So many things we have seen in the last couple of years have been pure sci-fi a decade ago. Switchblade 600, for example, has a loitering time of 40 minutes and a range of 24 minutes.
> and they barely move much faster than a carrier.
Fly in the direction bow to stern, low above the water. Or just ... loiter in the path of the carrier.