It's hit or miss with TSA at T4. I often use the AA club on the north side while flying WN on the south side. Always get asked if I know I'm at the "wrong" checkpoint, but only once had a problem. The B checkpoint is closest to "The Club," but all T4 checkpoints can get you there.

You are correct that you must go landside to change terminals, so leave 30-60 minutes to take the train to T2/T3 and reclear security.