You could also have it so there is a set pool of stages per game, with a ban from the losing player.
ex:
Game 1
Battlefield
Game 2
Rainbow Cruise
Brinstar
Yoshis
Game 3
Corneria
Mute City
Fountain
Game 4
Jungle Japes
Mushroom Kingdom II
Dreamland
Game 5
Kongo Jungle N64
Stadium
FD
Fox/Puff
G1: BF
Puff wins G1: Puff bans Cruise, G2 on Yoshis
Fox wins G1: Fox bans Brinstar, G2 on Yoshis
Puff wins G2: Puff bans Corneria, G3 on Fountain
Fox wins G2: Fox bans Mute, G3 on Fountain
Puff wins G3: Puff bans MK II, G4 on Japes
Fox wins G3: Fox bans Dreamland, G4 on Japes
Puff wins G4: Puff bans Stadium, G5 on FD
Fox wins G4: Fox bans Kongo, G5 on FD
BF-Yoshis-Fountain-Japes-FD
not a terrible outcome
Marth/Falco
G1: BF
Falco wins G1: Falco bans Yoshis, G2 on Cruise
Marth wins G1: Marth bans Brinstar, G2 on Cruise
Falco wins G2: Falco bans Mute, G3 on Fountain
Marth wins G2: Marth bans Corneria, G3 on Fountain
Falco wins G3: Falco bans MK II, G4 on Dreamland
Marth wins G3: Marth bans Japes, G4 on Dreamland
Falco wins G4: Falco bans FD, G5 on Stadium
Marth wins G4: Marth bans Kongo, G5 on Stadium
BF-Cruise-Fountain-Dreamland-Stadium
urgh thats pribad for Marth
Peach/Falcon
G1: BF
Peach wins G1: Peach bans Cruise, G2 on Yoshis
Falcon wins G1: Falcon bans Brinstar, G2 on Yoshis
Peach wins G2: Peach bans Corneria, G3 on Fountain
Falcon wins G2: Falcon bans Mute, G3 on Fountain
Peach wins G3: Peach bans MK II, G4 on Dreamland
Falcon wins G3: Falcon bans Japes (I guess?), G4 on Dreamland
Peach wins G4: Peach bans Stadium, G5 on Kongo
Falcon wins G4: Falcon bans FD, G5 on Kongo
BF-Yoshis-Fountain-Dreamland-Kongo
pretty freaking good actually
I personally don't like this idea (even though I brought it up lol) because I feel it would centralize the stagelist too much; the same 5 stages will be played every set for each matchup. I also think its too complicated for a tournament setting.
But if the goal is to take each set to a different, relatively balanced stage each game, then this works.