You raise an interesting question about software correction of the clock. Of course that is not possible in the sense of having a DAC tweak the control voltage on the internal crystal oscillator, because the SDG1000X does not have that kind of hardware.
However, even with the existing hardware it might be possible to adjust the parameters sent to the DDS engine in order to tweak the output frequency. So if, for example, the internal oscillator is known to be100 ppm slow then the firmware could change the DDS arguments so that it operates 100 ppm faster than nominal. Then the offsets should cancel. That would have the same result as actually adjusting the crystal frequency.
The offset data could be entered manually if one had measured the AWG's output against a precision frequency reference and noted the error, as you did. It might even be possible for the instrument to use its internal counter to measure a precision input and do the necessary calculations to learn the offset of its internal reference.
So it might be possible in theory. But probably not at the top of the list of things that the firmware team should address in the next release.
Maybe a more practical solution is to buy a $10 OCXO from eBay, build a little board that runs from a 5V USB charger, and use that setup to drive the rear panel reference input. One afternoon's work and you should be good to better than 1 Hz at 10 MHz. Maybe much better; depends on the OCXO.