Thanks cbxbiker61. That seems to have resolved at least half the problem. You were quite correct. I had (leftover from day 1)
rootfs / rootfs rw,relatime,errors=remount-ro 0 1
in /etc/fstab. I changed it to
/dev/mmcblk0p1 / ext2 rw,relatime,errors=remount-ro 0 1
and rebooted after 37 days of up-time. The system rebooted cleanly which it almost assuredly would not have done prior to this change.
I'm still seeing the 'not clean' indicator from tune2fs, though, so I'm left wondering how it will respond to a power fail restart. I'll have to give that a try at a later date. Perhaps the 'clean' vs. 'not clean' is a side effect of ext2 vs. ext3, as all my other root file systems are ext3.
In any event, on the basis of one test, at least clean reboots appear to work now, and that's a major hurdle. Thanks again!