Chastised by my previous failure in the battle against gross grout, I decided not to screw around anymore and to pull out the big guns. I took a trip to Target, where I purchased Soft Scrub Gel with Bleach. On a whim, I also shelled out a couple of bucks for a Scotch-Brite Grout Scrubber. The grout scrubber is generally the type of thing I would laugh at, but I decided to give it a try, since I didn't want to lose this round. Plus I didn't have any more old toothbrushes to use.
I came home and excitedly stripped out of my clothes (don't want bleach spots) and drew over all of the nasty grout lines with the Soft Scrub. I used almost a quarter of the bottle. It dripped all over, but all the grout was covered. As instructed on the bottle, I waited one minutes, then got in there with my grout scrubber and scrubbed.
And it did absolutely nothing. The smell gagged me, chemicals made the skin on the end of my fingertips burn (I really need to start wearing gloves), and I scrubbed until the little tool was spent, but everything is exactly the same amount of nasty it was before I started.
I think this is probably where one gives up and re-grouts, but if anybody has any other suggestions, I'm all ears.