Obviously fullback isn't one of the most critical positions, but I think Patrick Pass was a major exclusion based on the criteria.
Pass also had to switch positions to contribute, adding 35 pounds to bulk up to play fullback. He was a solid role player in the 2004 championship team, and 2005 was his best season. Below, a comparison of the 3 and their best season under BB:
Patrick Pass 2005 season
54 rushes, 245 yards, 4.5 YPC, 3 TDs
22 catches, 227 yards, 10.3 YPC
77 touches, 472 total yards from scrimmage, 3 TDs
Heath Evans 2005 season
51 rushes, 192 yards, 3.8 YPC
10 catches, 88 yards, 8.8 YPC
61 touches, 280 total yards from scrimmage
Marc Edwards 2001 season
51 rushes, 141 yards, 2.8 YPC, 1 TD
25 catches, 166 yards, 6.6 YPC, 2 TDs
76 touches, 307 total yards from scrimmage, 3 TDs