Just curious, but doesn't the modchip prevent the XBOX from going through the unlock routine? Otherwise how would it be possible to install off the self HD's in your xbox and never lock them?
Basically, what you originally suggested should work. Take your cousins HD out, put it in your XBOX, copy his C drive, put your drive back in and copy the files onto it. That sould give you all the original XBOX dash files so you can boot the original dash. There shouldn't be any need to unlock or lock either of the drives. However if that doesn't work, then you would have only wasted 10~15 minutes of your life, and you can try the method shanafan suggested.
However, If you do use the unlock/lock method be extra carefull that you don't end up screwing up both HD's by locking them with the wrong key.