The "R6" mod for the japanese gamecube requires you to short an otherwise empty resistor pad. This resistor pad goes between some pin on the ATI flipper chip and ground. It turns out that the reset switch also pulls to ground as well, when it is engaged, and that the region setting is only checked whenever a new disk is inserted.

Thus, if one is willing to sacrifice the functionality of their reset switch, it is fairly straightforward to convert the reset switch into a region select switch that only needs to be in the correct position when changing game disks.

After taking the gamecube apart, the following needs to be done:

Cut the reset wire on the board that holds the reset switch (this is the board that the game controllers hook into).

Run a wire from the R6 pad closer to the mounting hole on the gamecube motherboard to the pin marked as "1" on the reset switch. You can use the timekeeping 32.768 kHz crystal as a strain relief on the wire, so that it doesn't interfere with the heat sink pads when re-attaching the heat sink.

This is what the mod looks like in the end. I used standard radio shack wire wrap wire to do this mod, and a good fine-tipped soldering iron.

To operate the mod: you don't need to do anything if you want to play a japanese game. If you want to play a US game, hold down the reset switch while powering the system on until the game starts loading (ie, just after the gamecube "G" logo is done doing its thing). You can let go at that point and just play. I believe for multi-disk games you'll have to hold the switch down every time you put a new disk in.

Good luck!