Probably not a graceful or easy solution no. You could go in and edit the database directly to change it though. If you can find a ticket that is closed and has the proper value in the field it would tell you what you would want to use. Then it would just be a matter of looking to see who closed the ticket and updating it in the database. If you have a lot of tickets, or a lot of staff this could be a pain though.
You could also write a script that checks each closed ticket, looks up the last comment, checks the for that string in the closed by field, and changes the closed by to the person who made the last comment. This would require you to know PHP and MySQL though.
From taking a quick look at this, it appears that the problem that you are experiencing is that 1.7.x stores the staff_id when closed. 1.6.x did not. Although that would make it look like user 1 closed all of them)
table: ost_ticket
column: staff_id
If you dont care about your historical data being accurate you could change all 0's to 1's in that column.