How about you lose all cards that your opponent used when receiving a by first round. So basically you're cards are identical to the player you're facing if you receive a by first round.
Ehm...what???
Well you had a problem with it being an advantage to get a by since you would have more cards later on. So why not have the people who are having a by losing the same cards as the opponent they're facing?
In other words. Player X use card A,B and C in his first game and can therefore not use those cards again, player Y who received a by may not use any of the cards player X used first round, A,B and C in other words.