After I attempted to install the January Hotfixes via ITMUv3, the machine didn't reboot; but IE7 wouldn't launch, either.
Following the reboot, it seemed to take forever to launch, and it looked like IE7 was rebuilding. While it seemed to be stuck in this loop (it took so long I started thinking about "hmm... I think I have a recent backup of the data files") I remotely looked at patchinstall.log, and the ms07-004 had failed to install.
Laptop finally launched, and when I launched IE, it looked like IE6. Tabs were gone, the IE7 "look" was gone, it looked like IE6. But when I looked at Help, About, it said it was IE7. And then I remembered... I'm fairly certain this particular laptop was the one I installed one of the pre-release IE7 versions. I uninstalled IE7 from Add/Remove Programs, reboot, and instead of using ITMU to install IE7, just went straight to MS and downloaded whatever it was they wanted to offer me for IE7. Another reboot, and whew! tabs are back, all the fun alternate search providers are back.
Now I just have to re-run the ITMU patches; hopefully it won't lose tabs again!