Seeking update on delayed MacBook Pro battery replacement

I took my MBP in to my local Apple store for a battery replacement over two weeks ago. They said they would send it to California to be serviced. I got two emails two days later (Oct. 16) from Apple support stating they'd received my machine, and the second email said they needed more time to order a part.

Those emails are now 14 days old and I've had no update since. I'm wondering if the part (the battery, I assume) is back ordered, or if they have an estimate for receiving the part, or if the part came in and they are backed up on battery replacement repairs, or if my repair has fallen through a crack in the system somewhere.

I've called Apple Support four times to request an update. They give me the same information I already have: the status is In Repair, here's the case number, and the repair number, and a recommendation to contact the local store. Each attempt to call the local store routes me back to support and another iteration through the loop of explaining my situation and getting a similar response.

Is there anything else I can do? I've asked for an escalation path, and I was told to contact the store (which the phone system won't do, apparently). Would a Genius at the Genius Bar have any more information than the phone Advisors have access to, if I made an in-person appointment?

Am I just powerless at this point? Is there nothing to do but wait?