Update about immobilizer
Today I elected to have the VW dealer look into the Immobilizer misbehavior, which pretty much means they read the VAGCom and told me what codes were stored. I don't think there was any further investigation (but they did wash the car!).
There was, surprise surprise, a code for a failed reader coil. The coil is apparently integral to the ignition switch assembly, so you have to change a bigger piece than expected. It's $91. Labor is another $100. The part takes two weeks to arrive. I think I'm just going to take the suggestion given above and have a chipper delete that feature from the ECU firmware, rather than pay more to keep an unwanted system running, and possibly have it act up in the future.
However, before I send out the ECU, I intend to try some Stabilant 22 on the reader terminals. It might be interesting. I figure the self-test algorithm can't discriminate between a weak antenna and a troubled wire, and with the signal operating near 300 MHz, trouble with the terminals would be problematic. It's worth playing with.