However, given that I'm neither a non-EU citizen nor a Pole nor married, that isn't based on personal experience.
Just wanted to chime in on that count. I'm an American married to a Pole, and from what I was told at the immigration office after a lot of asking around is that I don't need a work permit since I have a Karta based on marriage. I *just* went through the process to get my second iteration of the Karta (the two-year one) as my first one (valid for only one year) expires next month. All is approved and well and no problems (I pick up the new card Friday), however I'm not sure if my school got a work permit for me or not... I don't _think_ they did but I'll ask and repost with the info.
Just *make sure* your card is based on marriage. There's nothing on the card itself that indicates whether it was based on marriage or employment, so you'll have to examine the approval/judgement notice that was given to you just before you got it for details. Otherwise hit the dreaded information room D and ask the nice people there.