Is it possible that this person was deliberately avoiding such statements of declaration?
I imagine myself, hypothetically, discussing physics with an opponent who only believes in Aristotelian mechanics. I'm not going to come right out and declare "Objects at rest stay at rest". Instead, I'm going to say "I believe that objects at rest stay at rest", going under a mock hypothetical that perhaps my belief is an opinion and not a fact, and then slowly try to win my opponent over. Making guarded declarations instead of absolute declarations is a common tactic of persuasion. (I almost typed "appears to be a common tactic of persuasion" in the last sentence, which shows how strong this tactic is.)
Given that, I find it possible that the person actually did believe that God exists, but felt that saying "Oh, and by the way, God actually does exist" would have been unproductive. She could have been trying to construct an argument that goes somewhat like this:
(1) I believe that God exists.
(2) I am an intelligent person, therefore my beliefs are true.
(3) Therefore, God exists.
Perhaps it was clear to her that you didn't believe (3), but she was holding out hope that she might convince you of (1) and (2), which would then force you to believe (3). If that is her line of attack, it would do her no good to declare (3), as it would more likely alienate you and make it harder for her to persuade you to believe (1) and (2).
I think there already is a New Improved Lottery that is played by many -- it's called drug addiction. Heroin addicts spend repeated minutes for their repeated fantasies. And their behavior at work or shopping is actually not that different from what you describe.
However, for us non drug-addled folks, there is a problem with sustained repeatable fantasy -- it doesn't exist. Buying one lottery ticket gets me one minute of fantasy, but buying 9 more tickets does not get me nine more minutes of fantasy, even if they are from different drawings. Lots of people dream about winning the lottery -- how many people dream about winning the lottery twice?
"I can cause you to invert your preferences over time and pump some money out of you."
I think the small qualifier you slipped in there, "over time", is more salient than it appears at first.
Like most casually intuitive humans, I'll prefer 1A over 1B, and (for the sake of this argument) 2B over 2A, and you can pump some money out of me for a bit.
But... as a somewhat rational thinker, you won't be able to pump an unbounded amount of money out of me. Eventually I catch on to what you're doing and your trickle of cents will disappear. I will go, "well, I don't know what's wrong with my feeble intuition, but I can tell that Elizer is going to end up with all my money this way, so I'll stop even though it goes against my intuition." If you want to accelerate this, make the stuff worth more than a cent. Tell someone that the "mathematically wrong choice will cost you $1,000,000", and I bet they'll take some time to think and choose a set of beliefs that can't be money-pumped.
Or, change the time aspect. I suspect if I were immortal (or at least believed myself to be), I would happily choose 1B over 1A, and certainty be screwed. Maybe I don't get the money, so what, I have an infinite amount of time to earn it back. It's the fact that I don't get to play the game an unlimited amount of times that makes certainty a more valuable aspect.
I can't help but notice that all of your examples are that which elicit negative emotional reactions. I think it might be illustrative to also have some examples of this fallacy for situations where the group X elicits positive emotional reactions. For example, wild deer are cute, and therefore any movement to kill them must be bad. Or, rape victims are all deserving of our sympathy, therefore any portrayal of a rape victim as anything but pure innocence is bad. (These aren't great examples, I admit.)