How deep into Jupiter would one fall before "splashing down"?

There was a question a few months back that mentioned Jupiter should have a solid core. It talked about the atmosphere gradient being significantly different on Jupiter than the earth, so how would this play out for an object falling into the planet slowly enough not to burn up?

Say we sent a strong enough probe in at a low speed would it eventually splash down into a sea of super hot, viscous gas? How deep would you go before that happened, and would it be a change so gradual there couldn't be a "splash", just a gradual slowing until you became buoyant?

Along the same lines, would there be anything like Ice IX deep enough into the planet, or is that sort of thing unique to water?

These threads are relevant, but I had hoped to spark additional discussion:

Skydive into Jupiter

Discussion of Jupiter's core