Huzzah!
That only took seven months.
I think leaving the country and coming back and restarting the process helped.
After I went back to Australia for SAGE-AU'2006, I had to get a new I-94 when I came back into the United States, and as the I-94 number is what the DMV was verifying my legal presence with the INS for ever and ever, I had to go back and get them to start again with the new I-94 number.
Seven weeks and one day later, my licence arrived in the mail. This concluded my bootstrapping - I have every bit of Government issued ID I need.
I think starting over was what helped. I asked a lot of questions as to how the whole "verifying my legal presence" worked. It seems they photocopy my passport, visa, and I-94 and mail it all off to the INS with a request that they sit on it for as long as possible. It wouldn't surprise me if it gets lost in the mail and/or they have no tracking for it, so requests can just disappear off into the ether.