Small radius solution?
Couldn't you move this back to a more simple setup (no tee, straight toggle) simply by reversing the ends? Larkshead the amsteel to the hammock, put the toggle on the top end going through the tree strap. Then you won't have small radius to small radius but have the wider area of a 1" tree strap against the small radius. I just like the idea of the smaller straight toggle over a tee.
Want to be able to disconnect from the hammock?... Use one of the dutch whoopie hooks on the hammock end instead of a larkshead.
I now have a reason to order up a knurling tool for my metal lathe, I'm thinking a fine knurling on an aluminum/ti round bar would eliminate any chance of slippage. Would be super easy to manufacture as well. And the amsteel is abrasion resistant (used in winch lines for a long time), and the tree strap is as well since the tree bark will be much rougher than a fine knurling.