I think you pretty much have the answer here but it continually astounds me that what is actually a straightforward problem seems to generate such fuss. I guess it's because one has to make explicit assumptions that are normally taken for granted or are "trivial". There really isn't any mystery at all, or any unresolved questions, as long as the problem is described with assumptions in the open.
So let's make the argument very compact.
SB has three possible strategies, given that by construction she has no information about where in the process she is or what may or may not have already happened. (A) Always guess H. (B) Guess at random. (C) Always guess T.
Two things can happen, with a probability of 1/2. (1) Heads comes up, and we talk to SB about it once. (2) Tails comes up, and we talk to SB about it twice (but she forgets the first time).
Now we can see pretty clearly that what we think about the best strategy depends on what kind of payoff matrix we have. Will she die if she gives a wrong answer? Then both A and C are equal strategies--50% chance of death--and B is worse with 5/8th chance of death. Will she earn $1000 each time she's right? Then her expected payoff is best with C, with $1000 expected winnings, then B with $750 expected winnings, then A with $500.
What if we ask: hey, SB, no payoff at all, it doesn't matter at all, but what branch do you think you're on? She never has a better than 50% chance of getting the branch right, but with a consistent "tails" strategy she does get it right twice in a row when she's on that branch. Do we care? No, we just said "doesn't matter at all". Were we lying? See payoff matrix calculation.
Now, if you happen to have a disembodied time-traveling and multiverse-hopping consciousness lying around that can possess other brains, and you ask that: please possess SB uniformly at random between all three times that I ask her about stuff, and then teleport/timetravel/universe-hop back here and YOU tell me which branch you ended up in...well...of course by construction it's 2/3 chance of hitting the "tails" branch, because that's how you roll when you're a disembodied time-traveling multiverse-hopping consciousness.
If you don't happen to have one of those around, you don't get to pick uniformly from all three times a question is asked, and so all you're left with is asking about the payoff matrix of two victories vs one.
So, to review:
* It's not a paradox.
* There's nothing more to explore.
* You can't sample all three "hey, what do you think?" events uniformly because the two actual-tails versions are 100% correlated unless you're our friendly neighborhood time-traveling disembodied consciousness.
* Because you can't sample all three uniformly, you're left to decide a payoff matrix where one branch has more events than the other, because that's how you constructed the scenario.
Corollary: correlated events are not the same as random samples, even if you don't realize they're correlated. What you don't know can correlate you.