Do you remember the hammock ropes origionally went straight through the edge of the hammock and then out and round the tree and back? If not say, and I will find a pic.
Well, my hammocks have always stayed up - since I learned how to tie the knot I needed with just one rope.
So....
I found some dyneema string - this is dinghy stuff that has a breaking strength of more than its thickness in steel, and tied it onto the rope with a sliding knot and pulled it through ( a bit like sewing the two ropes together and pulling it)
I then tied the thin stuff to itself and pulled it through again and tied a high tensile marine grade hook on it.