I'm not quite sure which part of the issue you are struggling with but here are three broad possibilities:

a. Separate screens for each of the four players located within the one activity, which might look the same to the user but which have different (i.e. player-specific) actionlists on the various buttons.

b. Separate screens for each of the four players located in different activities.

c. A single screen for all four players, with each button having a script which invokes one of four actionlists located on hidden buttons depending on which player has been selected. In other words, selecting a particular player sets a 'selected player' variable to a particular value and then each button script uses a switch statement to select the appropriate actionlist.

If you want your hard buttons to do different things for the different players, then option a. becomes much less attractive (because hard buttons are defined at an activity level).

Note that, in PEPv2, there is no such thing as "default equipment" for an activity. Rather, the whole idea of PEPv2 is that you can use any equipment in any activity.