Earning a living in analog IC design w/o an EE degree
The fastest route would be to get an EE degree, then a Masters specializing in analog IC design.  I can't imagine how you'd work your way up in less time, or that many companies would give you the opportunity.  Most analog IC designers have advanced degrees, and so there is a high barrier of entry.  A BS in EE actually provides very little in the way of analog IC design, and unlike things like programming, you can't really build an impressive resume hacking away in you're mom's basement.  The amount of money you have to drop for getting your own designs fabricated would be better spent on a degree.  Analog IC design is something where the "piece of paper" really comes in handy.  If you can't devote all your time to schooling, try getting a job at a tech company and go to school part time.  They may help pay for some of your education.