Just thought I'd point out that I went to Home Depot, and while they didn't have the exact part described in the first post, they had something similar.
It was in the plumbing isle, near the o-rings and other rubber parts that one would use to repair their faucets. It was a different brand (sorry I don't have the label with me), but was definately for an American Standard faucet.
The plugs themselves were nearly identical to the ones in the photo above, but were concave on the top of the plug instead of flat.
They seem to fit pretty well, although not as snug as I had hoped. They are just a little loose, but not loose enough to pop out on their own. When measured it looked like they were mabye 1/2" instead of 5/8" diameter, but there's a lip (its kind of ribbed) on it that might be 5/8ths and is probably why it's not coming out on its own. I'm thinking about wrapping a rubber band around it to make it a little more snug, but I don't think they're at risk of coming out or letting dust/mud in even if I don't.
Thanks for this idea-- it was raining the day I put them in and you can certainly see how mud and dirt would come up through them, there were already a few water streaks near the larger holes.