You can set it up like a double elimination bracket.
The problem with the standard double elimination bracket is that it assumes everyone who loses a match will still be participating. That will be the case here.
(I wouldn't cap it at 64, given that there are 128 losers coming out of the main bracket round 1. But I suspect it won't get to 64 anyway.)
Just to put some example numbers to what I'm talking about, here's what the setup would look like if roughly 1/3 of the losers from the main bracket joined the losers' bracket each round:
Round 1: 42 r1 losers -> 21 winners
Round 2: 21 + 21 r2 losers = 42 -> 21 winners
Round 3: 21 + 11 r3 losers = 32 -> 16 winners
Round 4: 16 + 6 r4 losers = 22 -> 11 winners
Round 5: 11 + 3 r5 losers = 14 -> 7 winners
Round 6: 7 + 1 r6 loser = 8 -> 4 winners (at this point, the main tournament has reached its semifinals as well and assuming a third place match won't be sending any more players here)
Round 7: 4 -> 2
Round 8: 2 -> 1
The main difficulty is dealing with odd numbers, but that can be handled with byes. I'd be happy to help with the logistics if that all sounds like a nightmare. ;)