I understand your point, but understand mine. Look at Bernie Williams' postseason stats. They'll shock you. He has 4 WS rings, made numerous All-Star appearances, won 4 Gold gloves, played CF for the Yankees, etc...and HE probably won't get in.
While Big Papi was/is a big part of the success of the Red Sox, playing DH alone certainly won't help his HOF cause. He would have to string together 10+ seasons of 35-40, 110-120 RBIs and avg. .300 to make that case overwhelming.
Walk-off hits are spectacular, but don't lend any additional weight. Check Joe Carter, Kirk Gibson, etc.