The GPS receiver is Haicom HI-203E. When the NixiChron had trouble finding satellites in 2010, I did reach out to Jeff about possibly getting another one. At the time, he responded with this:
"FYI, the receiver is programmed specific to this clock, and one purchased elsewhere will require all NMEA strings except $GPRMC once per second to be disabled."
The problem resolved itself and I didn't purchase a new receiver from Jeff. So, in all likelihood, the receiver I have is from 2005.
The Daylight Savings calendar is embedded in the NixiChron and since my unit is an older one, it doesn't have the firmware that's been updated with the new change-over dates. I remember waiting a month for the time to fall back an hour, which it did, but not long after that, the date has been wrong and the time reverted to Daylight Savings. This does sound like the rollover you're mentioning!
I don't have a way to check the GPS timestamp.