Oh, for heaven's sake. Now all of a sudden they show. Why???
The stuff I was doing was unrelated to the mod. I uploaded some test smilies and displayed them in a test post, then I deleted some of the smilies from the folder and from the smilies admin screen, only they were still showing in the test post even when I refreshed the page so I purged the cache like I've already done 99 times and after that I noticed the Facebook and Twitter icons were showing for the first time.
I'm so glad to finally have this mod looking right on my own computer!