A strong argument, well done.
This indeed puts me in a conundrum: If I answer anything but p=0, I'm giving a kind of weighting factor that destroys the supposedly strict separation between tiers.
However, if I answer p=0, then indeed as long as there is anything even remotely or possibly affecting my top tier terminal values, I should rationally disregard pursuing any other unrelated goal whatsoever.
Obviously, as evident by my writing here, I do not solely focus all my life's efforts on my top tier values, even though I claim they outweigh any combination of other values.
So I am dealing with my value system in an irrational way. However, there are two possible conclusions concerning my confusion:
or
This could be resolved by Omega offering me a straight out choice, pressing buttons or something. I know what my consciously reflected decision would be, even if my daily routine does not reflect that.
Another case of "do as I say (I'd do in hypothetical scenarios), not as I do (in daily life)" ...
I would like to point out that there is a known bias interfering with said hypothetical scenarios. It's called "taboo tradeoffs" or "sacred values", and it's touched upon here; I don't think there's any post that focuses on explaining what it is and how to avoid it, though. One of the more interesting biases, I think.
Of course, your actual preferences could mirror the bias, in this case; lets not fall prey to the fallacy fallacy ;)
Happy New Year! Here's the latest and greatest installment of rationality quotes. Remember: