ATP writes:

I would expect it to change somewhat, the air is not going to flow as
easily into a fully pressurized tank as it would into 0 psi. As it
turns out, it doesn't change much.

Yes, imagine a piston in a reciprocating compressor with leaf valves on the
output. Realize there is back pressure against those valves from the tank
pressure. The early portion of the piston stroke doesn't put anything into
the tank. Nothing goes into the tank until later in the stroke, when the
cylinder pressure first overcomes the tank pressure and forces the valve
open.

Surely we've all used a hand pump to inflate bicycle tires. Remember that
feeling that it didn't just get harder to pump against an almost-full tire,
but that your pumping strokes were of diminishing volume?

Why would it flow double the CFM at
a higher pressure?

Correct, the flow is strictly limited to the geometry of the piston
displacement, which is always the same, no matter what the pressure cut-off
is.