Be careful to have too much of a myopic focus on modern era quarterbacks. It's not just about passing the ball...
In the early era of pro football, fullbacks, halfbacks, and quarterbacks were essentially interchangeable. Look at the names again--they refer to how far behind the ball/line of scrimmage the players were. The fullback was fully behind the line of scrimmage, while the halfbacks were halfway between the fullback and the ball. The quarterback was between the halfbacks and the ball. All players were a threat to throw the ball or run the ball--essentially four modern dual-threat quarterbacks. (This is why the Hall of Fame lumps them together in pre-modern era football.)
These "quarterbacks" of the early days would've been comparable if not better to any of the players already mentioned:
Jim Thorpe (Olympic champion, played pro baseball, basketball, and football.)
Ernie Nevers (Signed pro baseball and basketball contracts, but starred in football.)
Dutch Clark is also an interesting story. As quarterback of the early Lions teams, he was so poor sighted, he had trouble seeing receivers, yet excelled.
I think one day Andrew luck will be on this list.