Cherry (Level 1)
You mean you don't think the almighty Dual Shock is God's gift to mankind? Seriously though, I have to agree. I don't like the controller either.
You mentioned it has only one less button. Actually it's missing four isolated buttons: there's no select, and the analog sticks can't be pushed in. Although you do have the digital clicks on the triggers that function as separate buttons, there's no way to press them on their own, and that could cause major problems with some games since you couldn't press them without first pulling the triggers. Another problem is that the only buttons on the GC controller that are pressure-sensitive are the triggers, so you wouldn't be able to use the face buttons properly on certain games, like racing games that use the sensitivity to adjust your speed. An Xbox adapter could be possible since it has the necessary buttons (which are pressure sensitive), but I haven't heard of any adapters for those controllers either.
All you can do is go third-party. An arcade stick is an option for games that use the D-pad, and would be better suited anyway for some of those games (fighters).
Peach (Level 3)
Xbox to PS2 adaptor:
Im not aware of a gc to PS2 adaptor either, so thats probably your best bet.
Yes, I happen to have one. It's a 10 ft controller extender with PS2, GC, and X-box inputs. It's made by "Game Elements" and it looks like a big hockey puck (for some reason I tossed the box, it probably came blister packed). In case you're wondering the Wavebird does not work on it.