I have resolved my problem.
I discovered my DVD/CDROM drive was not fully compatible with Windows 7, and was causing low-level hangs when any applications accessed it. In this case MM was obviously attempting to access the drive, but was also getting blocked -- and the process was hanging. This explains why the hung processes were so hard to kill: the hang was at a low device driver level.
Any process on my machine that attempted access to the DVD/CDROM would hang just like that exhibited by MM. It seems obvious to me now the DVD/CDROM was not functioning properly, but at the time I had just finished the Windows 7 upgrade, and had not put much mileage on all devices and applications. What is strange is the DVD drive worked well enough to do the Windows 7 upgrade. I guess the interim boot image drivers didn't have the same problem as the final OS drivers did.
My incompatible DVD drive is brand LG model GGC-H20L. I looked all around for updated drivers, but only found firmware updates. Turns out my drive is running the latest firmware anyway, so it is basically upsupported and worthless for use with Windows 7.
I replaced the drive with another drive compatible with Windows 7, and now my system and MM are behaving as expected.
Hope this helps anyone else experiencing a similar problem.