I don't even have to be put to sleep and woken up to do this. I can just say before the experiment starts that I choose to place 6 bets that the die will land on a 6 instead of 1 bet that it won't. — Michael

I wonder why you are so insistent on this arbitrary payout structure. Why not make an even-money payout on each occasion where she is being awakened and offered the opportunity to bet on the coin toss outcome as it is already determined right now? Would not her expected value exactly mirror—and be governed only by—her credence regarding the hidden die having landed six right now? A six is the most likely outcome, so I'm betting on it. No word games. Immediately maximized expected profit (and guaranteed long term profit as well).