Well, obviously there is no official solution. If you're asking what the result of Elga's method would be, you're right. But I would write "P(H and day 1)" not "P(H on day 1)", that can be confused with the conditional probability "P(H | day 1)".
I think Elga's method makes sense if one asks considers what Sleeping Beauty should do if she could bet on heads or tails (so that she wins 1$ if she is right and loses 1$ if she is wrong).
She bets on heads:
If the coin showed heads, she is right once (on day 1) and wins 1$. If the coin showed tails she is wrong on day 1 to 7, and loses 7$.
She bets on tails:
If the coin showed heads, she is wrong once (on day 1) and loses 1$. If the coin showed tails she is right on day 1 to 7, and wins 7$.
So it makes more sense for Sleeping Beauty to bet on tails and this would support Elga's method.