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You could hack the SQL file, but I would install a localhost version of MySQL and PHPMyAdmin. XAMPP is a popular solution which has a one-click installer. You should then be able to import the backed-up 'full site' SQL file into a blank database on your PC without risking your live site.
Basically, you create a new DB then select 'SQL' and 'Browse' to locate the SQL file and press 'Go'.
Having done that, you can select just the tables you want to restore to your live site (the AMS ones) and export those tables again as separate SQL files. There may be several to do.
You can then import each table separately into the matching AMS tables on your live DB using PHPMyAdmin.
If the AMS tables still exist on the live DB but are corrupt, press the 'empty' button in PHPMyAdmin. This clears out the table without deleting it. Then repeat the process for importing a SQL file as described above.
I don't have PHPMyAdmin on this PC and I can't remember the exact settings for exporting SQL, but if you Google 'PHPMyAdmin' there are plenty of tutorials that should be of help.
It may be a bit of work, but at least you have a backup
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