Contact cleaner did not work, nor did cleaning the contacts mechanically. This ain't my first rodeo and I know a bad switch from a dirty one.
I put in a genuine Switchcraft short toggle, not only does everything work reliably now, the feel of the switch is silky and luxurious compared to the clunky original, and it is utterly silent.
I have to say, I was pretty disappointed in the factory installation as well -- the wires were not inserted into the terminal's holes, they were simply laid against the terminals and stuck on with big globs of sloppy solder. The insulation on one lead was overheated and melty. I didn't bother desoldering, I cut the leads, cleaned them all up, trimmed, stripped, and tinned the leads properly, and got a mechanical connection before soldering. As it should have been done at the factory.