Ah, bugger. I've lost my link to Transparent Newcomb (TN).
From what I recall, Omega doesn't let you play the game if you would one-box on normal Newcomb but two-box on TN. As a result, having the strategy 'I will one-box on normal Newcomb but two-box on TN' will probably result in you getting no money because when Omega psychoanalyzes you, he'll almost always see this. So you lose, because you're not yet past the filter.
In this problem, you were filtered out prior to birth by a Prometheus who only chose embryos that he believed would one-box. The line 'I should one-box or I won't get to exist' doesn't work because embryos can't think. At the time at which you can first consciously consider this problem, you will be past the filter, and so are free to choose the most effective solution regardless of Prometheus's preferences. So you two-box and win, 'cause you already exist.
The problem changes, of course, if there is any way in which Prometheus could punish you for two-boxing, causing you to lose >100$ in utility.
Edit: Changed a couple of details to properly refer to TN when Omega has a slight possibility of being wrong.
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Aren't they all?
The super-powerful weapon...which cannot be used directly against the main antagonist...or is so evil it can't be used at all.
The artifact that gives only a subtle, unmeasurable boost to the hero's abilities...because the magic was inside him or her all along!
The magic whistle that summons help, only to be used in case of an emergency requiring its use...one and only one of which will arise.
The item presented by the old one to the hero who has a humble upbringing but newly discovered noble origins...which always casts insert backstory.
The useful magic item necessary to get the hero through a later challenge...which, when carried by a non-central character, always casts have item bearing non-central character carrying it get fatally wounded, but not so badly he or she dies immediately, and say, I'm dying, please take my item,' to which the hero says 'No non-central character, you can't die!'
The item that actually would kill the hero if used...which always casts insert villain arrogance, usually gloating and/or explaining the evil plan, providing time to avert the hero's death.
The powerful intrinsically evil artifact used by the villain...which casts karmic justice, turning against the villain, even though the hero was not strong enough (or too unwilling to kill) to do so (or kill the villain directly).
You might want to check out TVTropes.