With this hook, it has the product_id and based on the product ID, you can get the value of your custom field and it also offers the psot_id. So, what if you try to use the hook and based on the product_id get the value of your desired custom field and then assign it to your post based on the post_id.
I was having a problem with permissions for search results (searching by author triggered a "You do not have access to this page message) and traced that back to Defender Pro plugin.
Solution:
Toolset AJAX search feature is using wordpress built-in AJAX URL to send the request, for example: