I think you should get out of that nonsense. 18 teams is ridiculous - anything over 14 should go into two conferences with seperate player pools, IMO. The risk of collusion in this type of league is so great, I'd refuse to play - unless it is against the rules, you'll have all kinds of defenses and kickers changing hands in trades, and you're never going to know what deals were made under the table.
That being said, Bye weeks as a whole are going to be a dud. There just isn't a whole lot you'll be able to do about it anyway, so I'd just screw it. Hopefully, other owners will be wasting picks on 2nd QBs, Ks, and DEF, and you can load up on a ton of those mid-late round prospects. I would seriously consider trying to get my QB, DEF, and K on the same bye week and essentially forfeit that week.