There are multiple high quality solutions to add HDMI output to the Nintendo GameCube using a simple external pluggable device. Some of these include Insurrection Industries' CARBY and EON's GCHD MK-II.  Many of these devices originally shipped with older 2.4 GCVideo firmware and can not be easily updated to newer 3.x firmware.  I'm able to upgrade these devices to the latest 3.x version.  3.x updates also allow you to update the firmware yourself in the future.

A comprehensive install includes the following:

• Open the device and remove the firmware chip
  
• Upgrade the chip to the latest firmware
• Solder it back and verify operations