Thoughts:
Adding in a bye round does nothing to actually combat bad draws, it just gives one fewer game in which you can have a bad draw. Reducing the odds this way is not a solution. the only thing that can actually, fairly, reduce the bad draw luck factor is best 2/3. Unfortunately we don't have time for that, so if you get a bad draw in top cut then I'm sorry for your loss but it happens.
Top 16 is reasonable if you have time and 16 represents a MAXIMUM of 25% of the field, meaning a minimum of 64 players must show up to nats. any less than that and it should be reduced back to top 8. 16 is too many if only 40 people show up.
Allowing players to carry multiple decks in to the next round only works if you keep all of the top cut players segregated from each other and keep game results 100% confidential until players have picked a new deck. This would require game tables to be separated by a fair margin, players forced to remain seated until all games have been played and then choosing their next deck before they stand up again. It's easier just to make them choose 1 deck to carry for top cut.
Actually know that still doesn't work, when you get to the later rounds it would be pretty easy to tell who you're about to play. Especially when it gets to final four, you have a 50-50 chance of guessing who you're gonna play next. just make them lock in a deck.