TaskPaper 3 works just fine with Split Screen in El Capitan already. Nothing more needed.
Just press-hold the green traffic-light button and drag the window to one side or the other of the screen. Whichever side you drag to, the screen (behind TaskPaper) will be overlaid with a shaded area. Drop TaskPaper on either side of the screen. On the opposite side of the screen an array of large thumbnail images of the open windows from other apps will appear – basically the same kind of display as Expose. Click on an app’s “thumbnail”, and that app with then occupy the side of the screen that TaskPaper doesn’t occupy. This operation led to this result:
Text, etc., can be dragged from one pane to the other. Or just browse the panes side by side. Whatever. To quit this, move the pointer up to the top of the screen (as when exiting full-screen) and click the green traffic-light button again.
Not every app is Split-Screen enabled. Whatever you did, you did the right includes and flicked the right switches to make it work.