My guess is urgency. In those 19 years, the coach who had the most impact on the bye history was Fassel. The stats under his regime are interesting and revealing. The Giants went 1-6 under Fassel for the bye. The lone year they actually won was 2000, the year they went 12-4 on their way to the NFC Championship. This was a total microcosm of the post bye failure. The 2000 team was good enough and had enough leadership within the lockerroom (read Glenn Parker) to not give away a game. What happened the other six years? A combination of being much more ordinary AND Fassel being a player's coach who did not work the players hard enough. Fassel was famous enough for (at least some if not all of the years) giving the players a day off for each win they got before the break. They came back happy and fat. COMPLACENCY KILLS. When players have been interviewed about the reason/s for bye troubles, the common answer I have heard is that they were not ready or adjusted to the speed of the game.
Handley was 0-2 (Once again, SHOCKING! Not.) for the bye. Reeves and Parcells were a combined 2-4.