Spool goes on the descending module.

> would think the best option would be a somewhat high power radio transmitter/receiver.

If you can figure this one out, the militaries of the world would love to have a chat with you. Water/ice is ridiculously good at attenuating EM. It's a huge issue with submarine communications.

Wire-guided torpedos[1] and missiles[2] are fairly common, and the wire pays out from the projectile-side so it's not progressively dragging more and more. The more recent DM2A4 Seehecht torpedo[3] has a fiber-optic link, probably to reduce EM emissions or the detectability of a km's-long wire/antenna, despite being underwater.

[1]: https://en.wikipedia.org/wiki/Mark_48_torpedo

[2]: https://en.wikipedia.org/wiki/Wire-guided_missile

[3]: https://en.wikipedia.org/wiki/DM2A4

> I think your main issue will be that the hole freezes over behind you.

Getting an ice plug started is a problem, you need meltwater to get fast heat transfer from the melt-head to the ice, but you can't have liquid water at Europa surface pressure.

You'd need to take the cable spool down the hole, so the unspooled part above is already in place.