Read that Pats win against the Jags on strength of schedule no matter what happens. Worst case they tie and the Jags beat them head to head. So if true, worst the pats can do is the 4th pick. Two QBs will most definitely go in the top 4 so they get their 2nd choice of non QBs. That said, if they win they cost themselves atleast a high 2nd if not more in draft collateral for moving down a couple spots from 1 and getting the same player. No guarantees obviously.
IIRC, head-to-head doesn't matter in draft seeding / tiebreakers. And when teams are tied for losses, the draft spot rotates from round to round. If things stay as they are, NE would have the 1.01, 2.04, 3.03, 4.02, and 5.01 (they traded their own 6th rounder).