Is it possible to log edits within a date field?

A more sure fire way to log data changes is through a Data Change table.  Then you just have a button to change the date.

You also wont have to maintain a bunch of different forms with their form rules.

By creating a date change record, you automatically keep track of who, and when.  You can add a bonus feature really easy as to the why.

Long term this is the most efficient and cleanest way to track your date changes.

I can explain in more detail how to set this up properly if needed.