You most likely have a dead large cooling fan. They should both be running if the engine is hot, or if the A/C is on. If the small one only is running then you've got a bad fan.
But that's not your problem, or at least not your only problem. As posted above, TDIs don't make a lot of heat, and even in traffic in LA you shouldn't overheat because of a failed fan. At this point you probably have multiple issues, in part from continuing to drive the car. In order my best guesses (and they are guesses) are:
- Failed water pump (impeller isn't spinning, so coolant isn't circulating)
- Leaking head gasket (may not have been the initial issue, but it probably is now)
Failed gaskets I've experienced don't result in coolant in the sump or steam coming out of the exhaust. And the failure has to be pretty severe to get bubbling in the coolant bottle. Run your finger around the inside of the coolant bottle. If it accumulates soot, that's a sign of a failed gasket.
If you're going to replace the water pump I'd probably replace the thermostat at the same time, but it's unlikely to be a cause of your overheating. TDI thermostats almost always stick open.
You really should stop driving the car. The constant high heat cycles aren't good for it. At this point I suspect you need to pull the head, have it planed, replace the gasket, replace the water pump, timing belt system (as long as you're there) and thermostat. I doubt you have a rust in coolant issue. And use G13 coolant.
Good luck. If you know of Matt Phalen in the Bay Area he'd be my first choice for repairs. There really isn't, to the best of my knowledge, a good active TDI guru in the LA Basin. At this point I'd probably be reluctant to drive the car back north.
Good luck!