You can store additional information in the params column that's strictly for display purposes only and is how the modify date is already stored when an activity entry is edited by a user. You would likely need to store the original date there, but you will need to utilize PHP to do that as with the previous auto action suggestion. The below should extend the PHP I've already provided to store the current date as the modify date. You can also store it as whatever you want and implement your own custom display parsing for it.
Code:
$variables['var2']->params()->set( 'modified', '[var2_date]' );
$variables['var2']->set( 'params', $variables['var2']->params()->asJson() );
$variables['var2']->set( 'date', '[var3_date]' );
$variables['var2']->store();
That should set the current activity date as the modified date then update the activity date to the comments date. The modified date just shows as an icon next to the activity date though so if you want more customized display of that you'll need to implement it or store it to a different parameter like 'original_date' then add the display code for that in the activity_container.php template file.
Will review extending the Overrides parameters with a 'defaults.date' parameter to override the date display. The overrides can be found under the Parameters tab of an activity entry. Then you'd just store the original date there so it displays the original date, but sorts by latest comment.
forge.joomlapolis.com/issues/7173