You know, I'd never noticed that button before.If you open up a system view there's a little button on the bottom left next to the system name. Click it and it will prevent any of your ships from pathing through that system. It will also reroute trade. In the past, it was mostly used for systems with a Leviathan or Marauder or something so you wouldn't reinforce a fleet from the manager and then look to see all the reinforcements trying to move past the Dimensional Horror one at a time and getting eaten.
Unfortunately, it only allows me to restrict passage through systems that I don't already control, which doesn't help with my specific issue of trying to control my trade routes, but I'll definitely be using the feature for a few other things. Thanks.