So how many people do you think they need? You've said hundreds. At full speed they'd be shipping 400/week. So, you think they need roughly 1 full time person for each car shipped each week? So when Gen3 ships at 10x the volume, they'd need thousands?
I've worked at companies that manufacture and ship custom configuration hardware to dozens of customers a week (medical monitor). We were bound by regulation to respond with an investigation and filing a report every time someone died and our monitor was attached, which given it was a medical monitor often used in ambulances, that was pretty frequent.
All that customer interaction, the reports, etc? One guy with a couple assistants. If Tesla need hundreds of people to handle their current volume, that sounds like a devastatingly serious business problem. I suspect it's far more likely they simply have some crap processes to fix, which while also a bit scary, that's solvable.