Because he's slowly dying, and even he is starting to sense it amidst his deterioration. Knowing it's going to be soon, it's leading him to question whether he's truly going to be let into the pearly gates, despite the repeated assurances he was given by Murderchurch. Sure, he said the correct prayers, held the correct beliefs, and hated the correct reprobates...but how can *he* be certain that St. Peter isn't going to laugh, call him a lukewarm phony (Rev. 3:15-16), and press the gallows door that drops him into the lake of fire to spend eternity getting raped by Satan? This then creates a feeling of insecurity, which is causing him to scramble to "get his ducks in order" for when the inevitable kerplunk happens. Jack likely thinks that this endeavor will build his credibility with the man upstairs, and put him on more favorable footing for when the time comes.
So yeah..."Let me into heaven, Jeebus! I madeded you a hat and shirt!" is what it boils down to.