Excellent breakdown.
Despite all the so-called context that
@Ian and everyone wants to assign to Bill's terrible record (you can do that with everyone), your list conclusively shows that Bill was a sub .500 HC w/o Brady, which isn't the case for any of the other HCs you listed. There's something to be said of that.
Bill was also the HC & GM during his entire time w/o Brady, which not all of these other HCs were.
Finally, and this is more telling, Bill had 8 losing seasons w/o Brady. That's an extraordinary amount of losing. None of those HCs had 8 losing seasons in their entire career.
Lossing seasons:
Bill Belichick: 8 in 29 years (.276)
Andy Reid: 3 in 25 years (.120)
Mike Tomlin: 0 in 17 years (.000)
Mike McCarthy: 4 in 17 years (.235)
Tony Dungy: 1 in 13 years (.077)
Sean Payton: 5 in 16 years (.312)
Mike Holmgren: 3 in 17 years (.176)