I agree that neither of those counters is good for Allan Deviation. In general, ADev is a measurement that focuses on the short-term performance of an oscillator. You need a good counter and need to take lots of measurements. Maybe you should add a good counter to your list to Santa.
But your aging measurement is useful by itself. Don't try to convert it to Allan Deviation, just use it as aging. In general, higher quality oscillators like to be kept running and the longer they run, the lower the aging goes - within limits. Set up your oscillator with continuous power and let it cook. See how good it gets. The better the oscillator, the longer it will take to settle down to a constant aging rate. Some oscillators specify 30, 60, or even 90 days of continuous operation before their aging spec is valid.
Although your data isn't really appropriate for Allan Deviation, realize that there's no need to do the calculations yourself. The top software packages that do the calculations for you are Stable32, Timelab, and Plotter. All are free. Stable32 is the gold standard, but has a rather steep learning curve. Plotter is good, but the author has passed away and there's no support.
Stable32:
https://ieee-uffc.org/frequency-control/frequency-control-software/stable32/Timelab:
http://www.ke5fx.com/timelab/readme.htmPlotter:
http://www.ulrich-bangert.de/html/downloads.htmlAll will accept data from a file. Check the documentation for formats, etc.
If you really want to use this oscillator with a GPSDO, you should think about opening it up and adding the VCXO feature to it. Or just buy an oscillator that had the feature already.
Ed