Well, I’m afraid the only way in this case by making a direct modification to the core plugin code, but I am not sure if in that case it is possible, as the index table has a hard time working with exact matches.
Anyways, please try this modification:
1. Open the wp-content/plugins/ajax-search-pro/includes/classes/search/class-asp-search-indextable.php file on your server
2. Replace it’s contents with this
3. Save and clear all caches
If all goes well, this may boost the exact title relevances. Please be careful, I was not able to test this modification yet.