You're right that the comparison of real experiments such as Young's experiment or Millikan's experiment in the three situations (deep space, Earth, black hole) goes to the very heart of the general theory of relativity but your conclusion is exactly the opposite of the correct one.
The very basic postulate and fundamental principle of GTR, the equivalence principle, says that the three situations will have an indistinguishable impact on the lab experiments such as Young's or Millikan's experiment. If the labs were freely falling near the Earth; in outer space; or near the black hole horizons, they would see exactly the same thing in the experiments.
In the same way, if the lab isn't freely falling but instead, moves with some acceleration relatively to a freely falling frame, you may again prepare three experiments in the three situations that will proceed identically even though all of the physicists will feel some "gravity" (or "inertia": the same feeling).
In classical physics or special relativity, one talks about inertial and non-inertial frames. Only in the inertial frames (which include all uniformly moving frames relatively to a chosen representative), the laws of physics have a simple form. In general relativity, one may also talk about non-inertial frames, and because both inertial and non-inertial frames must use a generally variable metric tensor to describe gravity in general, the laws of physics actually have the same form in all frames, not just "inertial ones". In fact, in a generic curved spacetime, one can't find any "inertial systems of coordinates" anymore.
According to GTR, it's very helpful to compare not inertial frames with each other; but to compare all frames associated with freely falling observers. And the principle is that they will see the same physics regardless of the position or gravitational fields around them. They will always feel "zero gravity" whether they're in outer space, near the Earth, or near the black hole horizon.
Your basic template that "physics tells us that things should be different in the three situations" is just the opposite of what the important principles in physics tell us. Important principles, e.g. symmetries and their generalizations, are always telling us that certain observations are independent of certain choices.
