Hi Nick,
From what I saw on the Octoclock wiki page, it doesn't appear
to need GPS:
The OctoClock-G includes an internal GPSDO (GPS Disciplined
Oscillator) which provides an internal source for 10 MHz and
PPS from an OCXO high precision oscillator. Add a GPS antenna
(optional) with a clear view of the sky for GPS Disciplining
of the OCXO that futher enhances frequency accuracy of the
OCXO and global time synchronization.
Having said that, I still haven't been able to get the GPS to
work, but it doesn't seem like that is what is causing this
random offset problem.