20:20:14: Total frames encoded: 4664, total frames duplicated: 555 (11.90%)
20:20:14: Total frames rendered: 4364, number of late frames: 257 (5.89%) (it's okay for some frames to be late)
Well, there's the issue. Tons of dupes and lates, almost 20%.
Problem is, there's nothing indicating what's causing them. Video thread is under 11ms (60fps requires sub-16ms, so you're fine at 30), and CPU profiler is under 2ms.
There's a good possibility that this is just the Windows 10 game capture performance bug (welcome to early-adoption, and the teething problems associated). Supposedly there's a patch coming soon to try and fix it, When It's Done(tm). Not sure if going borderless fullscreen and window capturing would fix the issue, or if monitor capture would work in the meantime.
Alternately, some of the CLR browser/overlay stuff could be causing issues. Could you create a new scene with JUST a game capture of Battlefront and test-stream it? Never switch to a scene with any of the CLR browser or overlay stuff (that will avoid having it load; global sources only load the first time they're used in a scene). Run it for ~5 minutes. Then close OBS, reopen it, and upload latest logfile (have to close OBS for it to close out the current logfile). Can create a throwaway account for testing purposes (what I do). Not sure if this would do it, but ruling out vectors. Possible a slow browser thread could be throwing a monkey wrench in.
I don't think this will do anything and probably isn't necessary, but you might also bump up your scene buffering time to 700ms. It's the new default.
If I had to put money on, I'd blame Win10 every time though.