Your sketch shows much better than I was able to explain.
Initially, I just tied-off the outhall to the end of the boom, but my setup is now very similar except I don’t have a split control and it exits to a jaming cleat under the boom instead.
I’ve tied the ends off with a few inches spare to allow for wear & adjustment (I realised this summer that I was carrying about 10′ of spare line in the boom!).
My sketch isn’t quite up to your standard though!