Can you recommend at least one game in the adventure genre? I can't find a single game that fits this description as well as the original Zelda, but you made it clear that making a game like Zelda is not an option.

Hello! (Sorry for my bad english...)
Im not the host of this Jam but I would say, just to name some:
Monkey Island
Maniac Mansion,
Day of the Tentacle,
Hollywood Monster.
Indiana Jones and the Fate of atlantis
The Dig,
 The Whispered World,
Broken Sword,
The Syberia Saga

You should check out the top rated games from previous years. Much faster than a full game like Monkey Island :D

Zak McKracken And The Alien Mindbenders,

Beyond a steel sky,

Future Wars,

Cruise for a Corpse,

Detective Gallo, 

Leisure Suit Larry.