If I understand correctly, I don’t think the “give a bye whenever there’s an odd number of players in the round” approach would be very good.
Assuming there were the current number - 35 players - you’d have the following:
Rd 1: 17 games + 1 bye = 18 advance
Rd 2: 9 games, no byes = 9 advance
Rd 3: 4 games+ 1 bye = 5 advance
Rd 4: 2 games + 1 bye = 3 advance
Rd 5: 1 game + 1 bye = 2 advance
Rd 6: 1 game
That means there’s a bye in almost every round including someone getting a bye into the final game! That does not seem like the best approach to me. I would think you wouldn’t want byes beyond the quarterfinals. I think of the choices you’ve listed, you have to either run a normal 64 team opening round with most people getting byes into round 2 (your option #2), or keep it to 32 with alternates.
However, maybe there’s some other way to get it down to 8 teams with intermittant byes in the first 3 rounds that keeps more people involved throughout each round. I’m just vamping here, so this isn’t really well thought out, but maybe something like…
Round teams games byes Through to next round
Round 1 35 13 9 22
Round 2 22 8 6 14
Round 3 14 6 2 8
and from that point, you have a normal 8 team bracket. I think you could even set the brackets up in advance if you really worked at it.
Or maybe there’s even a way to get the byes all out of the way in the first two rounds, so nobody gets a round 3 bye. (11 byes the first round, 9 the second round?)
just some ideas…