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Jonathan_Graehl comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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The exact equivalent of the original problem would be as follows. You announce that:
(1) You're about to flip a coin at some secret time during the next few days, and the result will be posted publicly in (say) a week.
(2) Before the flip, you'll approach a random person in the street and ask about their expectation about the result that's about to be posted. After the flip, if and only if it lands tails, you'll do the same with one additional person before the result is announced publicly. The persons are unaware of each other, and have no way to determine if they're being asked before or after the actual toss.
So, does anyone see relevant differences between this problem and the original one?
I'm guessing you already understood this, but as a person accosted and informed of this procedure, I know it's more likely that I heard about it because the result was tails (than I was to hear about it before the toss). Those experiments that resulted in heads, I (most likely) never got to hear about.
So in asking if there's any relevant thing that's different, you expect a halfer to come forth and explain himself. Unfortunately, I'm not one. But it does seem to me that the only possible important difference is that Beauty knows about the experiment before the coin is tossed; but perhaps the amnesia compensates exactly for that.
As far as your "an instrument sold by a (so far completely ignorant) third party that pays off $100 if the announced result is tails", then of course Beauty would value it exactly as your interviewees, provided she knew that the offer was to be made at every interview.