Also, can I say that the PLC wasn't involved in the TYW and wasn't a part of the HRE (Prussia wasn't either). The only modern day part of Poland that was in the HRE at the time is Silesia. Just needed to clear it up a bit.
The PLC did try to instigate some intrigues against Sweden, including an alliance with Denmark-Norway, but those never amounted to anything. However, because of reluctance to go to war in the Sejm, Władysław IV was never going to be able to start anything. For this game, the PLC makes much more sense as an NPC that various players might be able to entice into providing troops, if they provide the funding.