Has someone considered the fact that the CLK signal is an output from the 3DS to the eMMC?
Bidirectional lines like the DAT0 are normally driven by open collector or open drain signals.
This means that the line has a pullup resistor to 3V3 and is pulled to GND by the device that wants that line to become low.
While the eMMC standard accepts multiple eMMC devices on the same bus, the 3ds likely isn't expecting something else taking over control of the eMMC interface.
So, basically, in normal operating conditions, the 3ds is controlling the lines. What happens if the 3ds can't access the eMMC? Will it turn of it's clock signal?
If you measure 2.xV on the clk signal, it's probably an average of the signal being switched between high and low. And as you aren't switching it, it's likely the 3ds doing it.
Most digital circuits that are not open collector or open drain survive when their outputs is pulled to gnd. They don't survive when there output is pulled or forced to 3V3.
So basically, we need to find out how we can stop the 3ds from generating the eMMC clk signals. When this condition is met, we should measure 3V3 on the clk signal (If our arduino interface drives it high as well) It wouldn't suprise me that forcing one of the other CMD or DAT0 lines low will disable the 3ds to eMMC communication (blue screen with error code) No idea if that turns off the 3ds clk generation. To proper see the condition of the clk signal, you will need an oscilloscope or a logic probe. You can even use the arduino bord to probe that signal. If you sample it several lines, and you measure high as well as low, it's likely constantly changing between high and low.
Also note that it could make a difference if you allow the 3ds to initialise the eMMC (only connect your interface after the 3ds was turned on) or if you don't allow it (connect your interface and turn it on before the 3ds)
Even if your interface is connected before the 3ds is turned on, it shouldn't influence the 3ds operation if all your interface lines are in the high state.
If you don't understand what I am writing here, you are experimenting on a dangerous level.
In that case I would suggest you use the raspberry pi as it has proven to work.
If you are trying to learn something and don't mind frying your 3ds, ignore previous sentence.