I got a technician's personal cell from his visit last month. Said he's willing to help solve the problem which is quite lucky for me and had engineering monitor my system this week. On the service side, I sent a pretty strong email about providing warranty work within 30 days (cited CA state law) yesterday and got them to also work with engineering. My app told me that service was ready to be scheduled this morning. Texted the technician a screenshot and he put me on his route next week.
The observation that Tesla Energy departments operate in silos with very little collaboration is SPOT ON. After PTO, you deal with service managers, engineering (indirectly) and maintenance technicians. Service managers and engineering seem to operate all over the country. Techs are obviously stuck in one region. Engineering will investigate and approve service, then service probably assigns techs based on their availability so you often end up with multiple visits with different techs each time. The techs end up re-doing eachother's diagnostics without the time needed to make progress. Then the service managers have to stall customers until they have to push the case back onto engineering to investigate (I'm assuming engineering hates everyone because nothing ever gets fixed, service hates everyone because nothing gets fixed and techs hate everyone because they never get to take their time and figure out the problems). Engineering needs to determine that maintenance is required and then service techs have to find availability for the next appointment (often with a different tech). Rinse repeat until you're lucky.
The goal, it seems, is to stay home and latch onto the tech that comes and incentivize them to come back if things don't resolve. Technicians have the ability to push things back onto engineering as well as Service. If things aren't resolved, get it's imperative pressure your tech and service to get another service visit approved by engineering. From there your tech should be able to schedule based on his availability and service managers should hopefully not meddle with your appointment.
TL;DR - You gotta play QB and push both CSRs and Technicians (get your tech's # and a give him incentive to go above and beyond for you) to get maintenance approved by engineering to get things done.