In my opinion, the most useful sorting method is by date of receipt. However, older mounts or mounts obtained on alts where the addon was disabled at the time of acquisition seem to be sorted alphabetically at the bottom of the list. It would be really helpful if we could fix this manually by entering a custom possession date. Alternatively, is there a way to modify the date in the addon files?

No need for any hacky stuff.
There exists already a command for that. Please check out /mje set date

I wasn't aware of that command thank you very much!