If I am understanding correctly, the problem is that the D10 pin on the LCD shield needs to be isolated from the base of the transistor so that D10 won't be looking at a base-emitter drop to ground if it goes high. If this is correct, seems to me that the easy solution is to remove the pin connected to D10 of the shield and replace it with a jumper wire with a diode or resistor. Then plug the jumper wire into the pin D10 socket of the Arduino. I think you could probably even just bend the shield pin in or out and plug in there too.
Am I missing something? Remember I am new to this world! I think would rather do this surgery than start scraping off the top of a circuit board or remove the LCD.
I don't think you are missing anything.
While your suggestion would seem to work electrically, I'm not sure it is possible mechanically.
There isn't much space once the shield is plugged on to the Uno and the pins are quite stiff in terms of bending
so I'm not sure you could make it fit/work.
The other h/w solutions in the thread are electrically the same as what you are proposing,
they just tap into the circuit by modifying the traces on the PCB rather than mess with the header pin.