@modad_MLBTS
This observation is invaluable.
It looks like two-way players are always killing it by late innings (multiple home runs + near-perfect game status), so the pitching perks would not meet the condition to activate.
So, for 2-way players to activate pitching perks, we would have to refrain from hitting home runs or scoring runs and hope our teammate doesn't do that when we're not batting.
As a game developer myself, I would say this is a design oversight that should be fixed. We are actually getting punished for pitching perfect games and hitting home runs in the same game.
My two-way player currently has a 0.00 ERA and is on a 40+ game hitting streak. So I guess I'll try to hit singles to extend my hitting streak, while not stealing or simply try to get caught to stop the teammates from sending him home.