Relay probes beneath the Schwartzschild radius

The Schwartzschild Radius (SR) was explained to me as that radius from
the center of an attracting mass M at which an object falling from
infinite distance will have transformed the gravitational potential
energy of (mc^2)/2 into its own motion. For a distant black hole, light
emitted from beneath this radius will not reach infinity - or
approximately - us.

Similar to calculating the potential from infinity to a radius, one can
calculate the potential from one radius to another. This likewise can
be equated to (mc^2)/2, the implication being that in the same manner
that light could not escape from the SR to infinity, it could also not
pass from some internal radius, to beyond the SR. I think this can be
repeated infinitely. That is, like an onion with infinite layers, it
looks like you can calculate consecutive internal radii from which
light could not reach the next outer layer.

The equation is, I think,

1/r = (1/R + c^2/2GM)

where:

r = the inner radius
R = the outer radius, beyond which light cannot pass, if emitted from a
lower altitude than "r".
c = speed of light
G = universal gravitational constant
M = mass of the gravitational body

My spread*** says the SR for a star having a mass of a million Suns
is about 3e11 meters (bigger than I expected - calculation error?). The
next layer of the onion is about halfway further inward, at 1.48e11.
The next at 9.84e10, etc.

The thickness of the layers falls off very rapidly. The first layer is
50% of the SR. The second layer is 67% of the first layer. The third is
75% of the second, and so on. (This looks like a familiar geometric
series the convergence of which I cannot remember. In the spread***,
it gives little appearance of converging.)

Here's my question...

We, located less than infinite distance from a black hole, should be
able to see light transmitted by our probe located just above the SR.
That probe in turn should be able to receive light transmitted from a
second probe located just above the first internal layer. Similarly,
that second probe should be able to receive light transmitted by a
third probe located just above the second layer, and so on. So
providing you could build enough probes and launch them toward a black
hole with the proper spacings between them, shouldn't they be able to
relay to you information from well beneath the Schwarzschild Radius?

A second question...

Is the frequency of light which is emitted from the SR red-shifted to
zero as measured at infinity?

Thanks,
ttnewton

ps: I did a search through the archives to see if this question was
already addressed, but did not find a similar post if it exists. Sorry
if I missed it.

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