I have a 21 inch dia, yellow poplar in my front yard next to house where I hang and test. And it takes a mim of 5' of tree sling,,if yu take a locked brummel loop and either thread thru your hammock end,,or loop tie it around gathered end,,then you have your 6' of whoopies to adjust for your length to hang hammock on each end. I carry but also have 8' tree slings, I normally do not carry the 8' ones but 2 pieces of amsteel 4' long each with a locked brummel loop on each end for extending my tree slings if need be, I normally use one biner per end to attach my whoopies to tree slings,,works easy and fast. that is your sketch your showing, Here is a locked brummel loop and how its made.
hope this helps. If you go west, and to national parks, you will need to protect the trees moreso than in a nat. forrest or private campgrounds. They will check you out especially Glacier, Yellowstone, Grand Tetons, and so on, I know they will check you in CA where ever you go there,,and the trees are huge in parts of CA. Sometimes 20ft dia is non exestince and you need more depending on where your wanting to hang so be prepared. For Glacier, I use with my topo maps, satillete maps as well to show the terrain.