Musicians, crafters of the Dope—how do I re-head this drum?

I’ve bee given a Peruvian drum to repair. It looks very similar to this.

I’m used to re-heading West Africa drums, where the skin goes under the flesh ring, then wraps around top of it and is held in place/tuned by the pull ring. Wiki diagram.
This drum is different because the skin goes over the flesh ring, wraps around it and is tucked underneath itself. The pull ring sits on top. Like this.

I have a few ideas, but none seems quite workable. Thoughts?