Okay I realize it's been some time, but I think I might know what you had wrong possibly?
I happened to plug my HDMI modded GameCube into an older HDTV (an old 42" Vizio with older HDMI ports). When I initially loaded it up... Super Mario Sunshine looked blocky as crap. I was thinking I had somehow damaged it moving it around, but then I found out what was wrong... For me, I had to disable the "Enhanced DVI mode" option in the GCVideo options. I'm not sure why or any of the details on this, so please don't ask me. However, turning "Enhanced DVI" off made it look remarkably better. I didn't test this with a lot of games, but it was a dramatic difference for Super Mario Sunshine.
For my GameCube, I get to it with a button combination, but I believe those of you using the adapter have to access it via a remote. Might check and see if it's on. If you turn it off and it improves... then huzzah!
Only problem with this is that "Enhanced DVI mode" is also the only way to get audio over HDMI. If you disable it, you'll have to plug in a regular Nintendo A/V cable to get audio out of it.
Hopefully this helps someone out who might be experiencing this issue.
Not sure if we're on the same page here. My
Wii GAME CUBE GAME CUBE GAME CUBE has the HDMI adapter. Yours is modded. I get audio output to TV just fine through the digital port, no setup necessary (still using default settings). Truthfully I haven't attempted to access the menu yet but hopefully my Comcast cable box remote will work with it.