Important for your experiment is the shape of the signal will be "the same" as the signal at the point S, but with much lower amplitude.
This is not true. We are not dealing with a transmission line. This is a totally different problem.
We are dealing with a divider where one impedance is a 2 k resistor and the second is a 50 ohm resistor in parallel with about 150 pf of cable and scope capacitance.
The signal at the scope is not an attenuated version of the SD input.
You just failed the scope probe lab above.
By the way, the capacitive loading by a passive scope probe has nothing to do with the scope input resistance. Look at the probe circuit.
The probe capacitance is:
Cp = (Cc + Cs)/(X-1)
Where Cc is the cable capacitance, Cs is the scope input capacitance and X is the attenuation factor. This is the the value of Cp required for frequency independent attenuation of X.
After the 2008 experience I bought a fixed 100X passive probe and it has a very small loading capacitance. In principle it should be about 2 pf but I think it is more like 3.5 pf because of extra stray capacitance.
Your way is better than my original 1X/10X probe that had almost 20 pf but not as good as my 100X probe. You just are making a poor quality 40X probe.
I couldn't use you method in 2008 since I was measuring a signal on a shield. I couldn't probe the GND end of the resistor. Guess your way wouldn't have helped.
Edit: I got a better result with your method by not using any coax. I just put a 50 ohm feed through terminator in the scope and connected that to a BNC with short pigtails. I put the Arduino with the resistor divider right next to the scope. The rise time then looks like I expect. This eliminates the cable capacitance and only leaves the 20 pf scope divided by 40 or almost nothing.