Put the cable reel on the probe, so any cable already laid is stationary.

The problem is that, on earth at least, ice moves. I'd think there'd be a pretty good chance of the cable snapping before the probe tunnels all the way through.

Then there's the question about the weight of a transmitter capable of broadcasting through 30 km of ice vs the weight of 30 km of cable (and figuring out how to make the cable reel reliable under those circumstances). Of course, there's the corresponding problem of knowing the makeup of the ice (particularly whether it's an insulator or a conductor).