I (embarrassingly) have this same problem and cannot sync my calendar. I have found some other posts with Calendar.apk and .odex files for other phones; will these work across phones running JB 4.1.2? I tried putting them into system/app with a root browser, but after a reboot they were still not installed.
I have a rooted Razr M but did not boot unlock it before I accepted the OTA, so no unlocking for me unfortunately. Any suggestions/anyone have the .apk and .odex files necessary to re-install the stock calendar?