My design uses a CR network but this feeds a HC14 Schmitt trigger inverter which then drives the microcontroller RST pin.
NO, that will not do. A schmitt trigger is NOT defined a the very low voltages occuring at power-up, a supertvisor is.

Get rid of your supervisorphobia!!!

All the failing devices have a date code of 0110 (2001 week 10).
which jives with your design being marginal and not handling devices which are to one side of (but within) the tolerances.

Erik