The best way to get in touch with a service center via phone, is to call the number listed for the service center, and listen very carefully to the prompts. What you want (are listening for) is "checking on a vehicle currently in service".
That actually rings the local service center that (presumably) has your car in service. Of course, the person on the other end, at the service center, will be expecting to talk to someone who has a car in service, or a situation like this OPs where they need almost immediate help (and its not "my battery has 7 miles less than it used to, teslafi says.....")
Anyway, thats how you get through to a person in the service center. pretty much every other option rings a call center. In this specific OPs case, since he had already scheduled an appointment properly through the App, an escalation in the manner above would have been well received by the local service center.. they would have done the same thing over the phone that they did for OP in person.
In other cases, unless its fairly clear to them why you circumvented the app when you (presumably) dont have a car in service, they might be a little more brusque (lol).