You're gonna need a bigger hammock
Why use rope? If you have enough between the bad spot and the hammock tie a pair of descending rings in with a clove hitch. Use a long piece of 1" polyester webbing with a loop in it. Run the webbing through the loop then tie a garda hitch in the rings. Better yet use a Dutch Clip at the tree.
spelt, welcome aboard from Florida. Before doing too much start off with the sticky's in the suspension section. I've only been here six months and have found that hanging is a fluid and ever changing endeavour. We are a bunch of experimenter and are not set on any one way to accomplish something. Stick around and I'm sure you'll be playing with yours, hammock that is.
Most of us end up poorer here but richer for being here. Olddog, Fulltime hammocker, 365 nights a year.
The damage, I believe, is caused by the rings.
The rings work by squeezing the rope, and that essentially causes damage.
Skip the rings and go with the suggested whoopie slings.
Several vendors here on the forum offer them for sale.
There are several threads and videos showing how to replace and use the whoopie sling, as well as how to make your own.
Ambulo tua ambulo.
If you do hang from that rope, be sure to film it for youtube.
Silver on the Sage, Starlit Sky's above, Swingin' from the trees in a Hammock that I love.....