You don't need a hard connection on both ends, or even one of them, really. Lag some blocks to the tree, and rest a floating box frame beam that encircles the trunk on the blocks. Unless trees really sway, it doesn't even have to go all the way around- a frame like a section of ladder would work. As a kid, we did floating supports for multi-limb treehouses like that. Tree could still flex with no problem, and the treehouse never got overstressed. For ease of construction, a couple long 2x6s or 2x8s in parallel, with cross-pieces to make them nice and stiff, maybe slanted in alternating directions so they make box sections but still drain well. Viewed from side, minus top and bottom edges, since I suck at ASCII art: I / \ / \ / \ / \ I . Put the beam together with deck screws, and hang swing from threaded rod run through both sides of beam, or from short 2x6s run flat across the top. As long as trees never sway so much that they spread enough to make the beam fall off the blocks, it should hold up longer than you do.
Legal disclaimer- use at your own risk. If you kill somebody with this design, remember what you paid for it. I am not an engineer or architect, blah blah blah.