I thought the smell of electronics and blower malfunction was more of an indication of a blown blower motor.

You should try and test the blower directly. Here is a write-up on the the E39, but look around for a write-up on how to test the blower on an e53.. I have replaced the blower on an E39 and sure would rather not do it if I don't have to.

https://www.pelicanparts.com/BMW/tec...or_Testing.htm