Such a simple idea, so complicated in execution...
So I did a bunch more online research, including correspondence with a guy who seems to know everything there is to know about rope, and ended up with some really great stuff:
This is a 12 strand polyester rope for the forestry and arborist climber. Firm construction meets the demands of the professional user. With its white color and red tracer, this rope is perfect for climber who wants a great traditional rope.
1/2" x 150 ft. Forestry Pro 12
7300 lb breaking strength
Then came tying it to the clothesline (that we have had looped over the branch where we want the permanent rope/ swing to go) and trying to hoist it up.
Not so fast.
We could hoist it up there fine but it just would NOT go over the branch. Kept getting stuck on the bark or something, absolutely not budging. We did all kinds of stuff -- I made this complicated streamlined thing with duct tape, etc., ain't gonna happen.
We spent a fair amount of money on that rope and love this idea so we called the tree guys and asked how much it would cost to have someone come back, climb up there, and pull the damn rope over. The tree guy said he still liked the idea of an eyebolt better -- healthier for the tree. We'd discounted that because the damn branch is 75 feet up, but if we're having someone go up there anyway...
So we're having the eyebolt installed (one of the tree guys will do it in his spare time to make some extra money, not so bad), and then hopefully we'll finally have a good, strong, long-term tree swing.