Create a new optional header field to indicate when a reply is expected by. Since this is a non-standard field it would be for use by the sender and any Thunderbird user receiving it. As a non-standard field it could contain any characters but, to be usable, would have to conform to standard date-time format.
This could be used in a number of ways:
Put entry in calendar for expected date to check;
Create a list of replies expected (probably in date order);
Create a list of overdue replies.
A reply should link to the list or calendar entry but there would have to be a 'valid reply' or 'acknowledgement' box when reading the email to enable the user to continue or close the entry. Ideally there should also be some way of linking a reply which does not contain the original message-id when, for instance, they reply by snailmail.