OP, Remember, while TAM hasn't been fully integrated to the Star Alliance yet, redemptions with AC/Tam can be made with your AP points, albeit only via the AP call center (and yes the 30$ booking fee would apply).
So you might be able to make a booking for the dates you want using a combination of AC and TAM, for the minimal amount of points required (I believe the redemption chart is the same as AC, 50,000 for Y, 75,000 for J).