For I am a sinner in the hands of an angry god

This meaning drifts from the cocktail to the person/game... But I don't recall a meaning of bloody mary where the person hopes they die soon. Is this a reference that I don't get? Or is it some sort of alcohol-related depression? Because I feel like they just lost sight of their metaphor.

I also feel like there is a missed opportunity to have the entire prayer just list ingredients. You know, like bloody mary full of vodka tabasco be with you blessed are you among cocktails and blessed be your fruit or vegetable or whatever, tomato juice.

Think it's just about the unpleasantness of hangovers

That makes enough sense that it must be the answer, but I feel that it doesn't really work as the author intended, since that is a huge complaint about it. They just said that it was blessed among cocktails.

I'm afraid if I stop drinking all at once the cumulative hangover will literally kill me.

It’s from the show archer and makes perfect sense in context. He’s an alcoholic, with a hangover, drinking a Bloody Mary as a hair of the dog thing (drink the next day to make the hangover less intense). The video is linked elsewhere in this post.

Bloody Marys are traditionally a cocktail you drink when already hungover. Takes the edge off.