Sigi,
I guess you are mainly seeing the short time (in)stability of your TXCO and not the (in)stability of the beacon sync loop, double-check with beacon sync disabled.
With an decent OCXO based reference, the short time jitter is around 1Hz with beacon sync enabled and <1Hz with beacon sync disabled. Knowing the Allan deviation of my reference, my guess is that a noticeable part of the 1Hz is due to the transponder and/or RF path.
73 Jean DJ0VL