I have a similar experience with a HP 5385A with option 004 (oven heated oscillator). After testing I could see (by comparing it to another OCXO in my HP8656B) that it was drifting with temperature, indicating that the heater element is probably defect. Touching the OCXO while powered on, confirms this – it has the same temperature as the surroundings.
This week I received a GPS disciplined 10 MHz frequency reference (Symmetricon TrueTime 600-00 XL-AK). Using that to trigger my scope, I clearly see the drift of the 5385A, while the 8656B is rock solid.
My plan is to use the Symmetricon as a common freq. ref. for all instruments, but that limit my usage of the 5385A to my bench, so I am considering changing the OCXO anyway.
metrologist, did your repair go as planned, and did you find a OCXO that actually fit into the 5385A? I assume, that the OCXO must be tunable, to be sure to get the high precision.