Personally I would stay at TBIT. LAX Polaris lounge (PL) is the weakest of all PLs in the system; and while *A lounge has deteriorated a bit, it is still very good. In other words, I don't think PL is worth the round trip given OP's available options.

TBIT the terminal is also a great place to hang out even without lounge access...something you can't say the same for other terminals on the south side.