So all the oil unloading facilities in LA have been shut in now for nearly a week. Is it logical to presume that would cause a glut in the world oil market, eg. tankers already at sea and heading for the gulf now looking around for another port, anywhere near, to unload at any price?

Interesting thought. Where does the oil that can't be refined in the US go?

I would imagine that they would divert to Houston or the US Atlantic Coast in the first instance, with other options being the refinery on the USVI ( a big products supplier to the US ), Rotterdam, or refiners in Europe.

I suspect that products will be a bigger issue than crude over the next couple of weeks.

Except that, if it was a supertanker, it would not be able to offload at either Houston or the US Atlantic coast directly.

The TOPS project is a couple years out, at least. That would at least provide some redundancy, and/or something else to wring our hands over during hurricane season.

Europe is an unlikely destination - the current oversupply in the North Sea has caused the Brent curve to move in an even steeper contango than WTI, with the prompt contracts trading well below WTI levels. If they can't unload, VLCCs will just slow down - the steep contango means that suppliers have nothing to gain by getting crude into ports fast. Remember, every barrel of crude stored for a month earns you $1.40.