Since at the event horizon (schardzchild radius) time dilation becomes infinite, essentially time ceases there. That's why it's called an “event horizon”: because events (four-dimensional coordinates) become disconnected there. As time is frozen (from an external observer's perspective) stuff ceases to move and just “piles up” there. From the in-falling matter's perspective, however, the transition occurs in finite proper time. Once it has crossed the horizon, it finds itself inside the hole where the direction of space pointing towards the horizon (inwards) becomes ‘timelike’ (in the sense that its flow cannot be arrested and it is unidirectional) and time becomes ‘spacelike’ (in the sense that it could be negotiated at will).
No experiment that I know of could confirm this because everything will depend on extrapolation from less extreme and finite scenarios.
You could go into the black hole yourself but you'd need to communicate the results of your experiment by twitching the second hand on your daughter's watch who, conveniently, works for NASA.
Interstellar infuriated me worse than the average “space opera” Star Wars/Star Trek-type crap because it spread the pretence of being scientifically accurate and plausible.
Before we get to the black holes part... why didn't they have timestamped signals from the surface of that water-planet? Why didn't they go into a polar orbit (as opposed to equatorial orbit) around it so as to minimise the cumulative time dilation around the black hole it was orbiting? What kind of specific impulse were they supposed to have to be able to take off from it after they'd landed.
Oh, I cringed. I cringed so hard. Poor Kip Thorne.
In the first place it is just ridiculous to envision settling humanity on to a planet so close to a supermassive black hole & experiencing such extreme time dilation. It was foolish to have sent an astronaut there at all, let alone the later party going to check on her. But then, Kip Thorne confessed that Miller's Planet was essentially something the studios demanded and he wasn't given an option to exclude it. He wasn't even given an option to make the time dilation less extreme.
No experiment that I know of could confirm this because everything will depend on extrapolation from less extreme and finite scenarios.