I'm the author of the answers in the thread you linked to and I'm afraid that's a different situation... In that thread the goal was to have one origin and two targets where one target was the included list and the other the excluded list.
In your case you're wanting selections in the active roster & taken players to both be treated as origins with the single target of the available players. The way Tableau's actions are designed is based on the target dimension(s)...if the target dimension is the same for two different origin sheets (whether using one action or two) then the dimension filter is overriden by the most recent selection. This makes self-iterative interactivity with filter actions extremely difficult to generate. Also filter actions are triggered by clicking on marks, whereas in the view you provided the goal is to use quick filters to make the player selections and unfortunately quick filters don't trigger mark selection.