Have you tried to call in to A3 to get the mileage ticket booking done over the phone? I doubt it works as well nowadays as it used to when some of this kind of stuff used to happen years ago, but it’s worth trying.

The award flight availability discrepancy (between programs) is a problem that is only getting worse and worse for intra-alliance flights. [Unfortunately, it’s not just an issue limited to Star Alliance — it’s part of a more general trend across the industry.]