Geoff,
Unfortunately the 3560/3750 switches do not support TFTP in rommon. I will suggest bumping up the speed when using xmodem for file transfers. Using this will take less than 10 minutes for a file transfer.
in rommon (case sensitive)
set BAUD 115200
change your connection speed in hyperterminal, and start transfer.
to change it back after the transfer
unset BAUD
and it will go back to 9600. Change the settings back in hyperterminal and boot.
This will save lots of time for you.
Mark