Are you a coder? do you know how to work with WordPress hooks & filters?
If so, this is what I would do,
1. Everytime a request is made to submit the post form, hook the CF7 plugin wpcf7_form_hidden_fields
to add a hidden field to your form (prior to it being loaded/displayed). and add a hidden field to your form with your product owner user id.
2. In the plugin mapping editor, use the post author field ‘Hook with a function’ option and copy the provided filter function to your functions.php file. In this function, use the subitted hidden field user is to set the author id.
If you are not a developer, then I suggest you hire one (or myself) if you have the budget for this.