How to repair an old Mayan hammock

I am trying to repair an old Mayan/Mexican hammock that had several strings snap after many years of use. It is a thin-string, fine-weave variety, made of cotton.

The snapped strings are in the lowest area where most of the weight is when lying in the hammock and I cannot figure out how to properly weave them back in. Is there a way to do this or possibly remove an entire "strip" from the hammock getting rid of the problem and everything around it?

Other "fixes" are welcome as well. Anything that would keep me from having to just throw it out.