Thanks!
I have installed the plugin, and looked through it’s code for a possible usable API. I have found a solution, which will probably work. But please note, that this is not an optimal solution whatsoever, and I am not sure how will it affect the overall search performance, but this is the most I was able to achieve within a reasonable timeframe. While customization is not part of support, I was trying to get the best out of this, as possible.
Add this custom code to the functions.php in your theme/child theme directory (copy from line 3 only!). Before editing, please make sure to have a full site back-up just in case! This code will alter the search arguments, to allow only post IDs which are meant to be seen for the current user.
I really hope this helps!