While it is true that hiring a coach under contract with another team typically requires a first round pick, I don't see the Giants giving up a top 2 pick. They need a QB almost as badly as New England, if not more so.
There's a few things to consider here. First, we know that Bill is on good professional terms with Brian Daboll. He is not going to do anything to undermine Daboll while DB is still with the Giants. It's also quite possible that Bill's opinion of the Giants could be colored by the experiences of both Judge and Daboll.
The other thing is that there is probably only a couple of places on the east coast that Bill would move to. He's got a lot invested (both personally and financially) in his residences on Nantucket, so I don't see him moving cross country, unless he really becomes singularly focused on chasing Shula's record (something nobody really knows right now). Jets bridge is permanently burned. Eagles aren't moving on from Sirianni anytime soon, nor are the Dolphins looking beyond McDaniel. Bills are a possibility, but their roster is getting expensive real quick and windows of contention can slam shut overnight. Carolina (still rebuilding from the studs), Bears, Green Bay (QB is probably worse than Mac), Falcons, Titans, and Giants are the other eastern/northern central teams that could be looking for coaches, but unclear which ones would intrigue BB and vice versa.