Did you read about the Gullstrand-Painleve coordinates? They can be interpreted as space flowing, which seems to be what you are talking about.

That looks like a very simple calculation, so why not check if you get the same results or not?given by the difference of escape velocities at these heights, √(2GM/r) and √(2GM/(r+h)) respectively.

so I am sure we'll get the same results.