Here’s a suggestion from one of my other hobbies: if you are looking for a simple 8-20V variable voltage AC power supply that’s not regulated, rather than rigging something up yourself you might want to consider just buying a used Lionel model train transformer. Although most are now 50+ years old, they were built very solidly and most work just fine today. Most (although not all) have a circuit breaker in them and some are even U/L listed. And if something is wrong, they’re easy to repair with specs and parts readily available.
You can pick up a single control 25-75W unit for +/- $10 on Ebay. I keep one on my workbench for testing train equipment but also use it from time to time in my electronics as well.