I hear 7/8 all the way through.

Because I can't remember how to phrase an up beat in an */8 time signature, think in terms of 7/4 for a moment. You can clearly hear the repeating percussion pattern on these notes throughout the entire track:

1 & [rest on 2] & 3 4 & [rest on 5] 6 7

I distinctly hear 7 downbeats each bar.