I used Josh’s method for a test run of bricks. They got pretty clean, but the LEGOs all bumped up against one another a million times, leaving lots of micro-dings on the smooth surfaces. I compared them to the other bricks which I had not washed. The other bricks also have micro-dings, but I believe the ones I washed have more, or more prominent, micro-dings.
Now I’m thinking about maybe trying the dishwasher, where they would not be moving around.