I took a different reading of OP's question, hopefully this will help:

- You can buy a day-pass for AA's lounge at $50/person, but at that price you might as well buy a 30-day pass for $99, which includes one guest accompanying you.

- Your AA pass won't give you entry into the OW lounge at TBIT.

- You do not have to be flying AA or OW to use the AA lounge (in fact, you don't even have to be flying at all, under some circumstances).

- You can buy the pass at the lounge or online.

- You CAN access T4 with your CX boarding passes so you can use the AA lounge, but indeed there is no airside connection. It's a short walk from T4 to TBIT but security at TBIT is unpredictable and could take a while to clear.

If I were you, I would pursue the Chase Ink/KAL lounge option as the easiest, but worst case scenario, the AA lounge is an available option.

Also, have you been inside TBIT lately? Much improved terminal.