I found a decently somewhat sometimes consistent setup for CLUB MED as the opening puzzle.

In addition to stepping on the p2 controller to hold A, I am also holding Select+A+B on the p1 controller during player name entry through puzzle selection. The way controller inputs influence the RNG is wild, not only did Club Med open the run as expected but the next 3 puzzles were identical to my previous PB.

CLUB MED THE MONKEY'S PAW CORNUCOPIA SLEEPING BAG

Someone will eventually fully manip ideal puzzles for all 4 rounds.