I'm just one of the many Ice Tube Clock hackers out there, but have no relationship to Adafruit. I did write the xmas alternative firmware back in the day, so I guess you could say that I have some familiarity with it. ;-)
You can tell if your version of xmas has GPS support compiled in by toggling through the menus. In the menus, select "cfg regn", and go through the list of submenus. If you see "set zone," then your version of xmas includes support for the GPS mod. Unfortunately, there is no way to see the baud rate for communication. The default in xmas is 9600 which works with the Adafruit Ultimate GPS module, but you'd have to ask whoever provided your kit if they left the default in place or changed the baudrate to another speed.
Xmas only runs on the atmega328p chip. It's too large to fit on the 168v and also uses the picoPower features of the 328p for extra sleep efficiency. So that's why you have a different chip.
With respect to the clock circuit, the Adafruit design would often lose about 2-3 seconds per day with the default 20 pF caps--at least in my experience. Reducing the capacitors to 10 pF increased accuracy on the few clocks where I tried that. But with a clock drift of 2 seconds per hour, you might have a slightly damaged crystal. Here's an excerpt from the xmas firmware/REAMDE troubleshooting section:
Finally, replacing the crystal will sometimes resolve the issue. The
replacement should be another 32.768 kHz crystal with a 12.5 pF load
capacitance and equivalent series resistance of 30 kOhm or less. The
AB38T-32.768KHZ is a good choice and is available from Digi-Key or
Mouser. When installing and soldering the crystal, gently push the
crystal through the circuit board until there is 2-3 mm of space
between the bottom of the crystal and the circuit board. Leaving this
space prevents undue stress on the leads which could damage the
crystal; it also ensures solder will not make unwanted electrical
contact with the metallic crystal housing.