When I think of sock, I'm referring to something like this:
It's akin to the strainer at the bottom of your pump. The main/real filter has a much finer rating.
I gather that yours cranks fine and does run for a bit, so I'm dubious of stator problems. You could check the voltage at the O/W lead of the dealer mode connector. But it ought to be OK.
It's harder to do but you can check the level sensor with gas in the tank. Unplug the electrical connector and measure the resistance at the contacts with the sensor fully raised and fully lowered. But be careful that you don't break/bend things when submersing the float.
I've been focusing on "clay looking crud" but gather that there was a bunch of rust on the inside of the tank. That didn't come from the hurricane. You need to spend some time getting all of it out by mechanical and chemical means or it could clog your pricey new filter. There are many such threads here, this
being one of the more informative ones (it's long).
BTW, if you have a US model, it doesn't have an immobilizer. They have a special indicator light on the cluster that blinks when the ignition is turned on. See the service manual for more info.