As you probably know, there is no consensus which is the right solution to the original problem. Some people, including Adam Elga say it is 1/3, other people including David Lewis say it is 1/2.

If you're asking what the result of Elga's method would be, you're right, it would be 1/8. 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)".