Hi,
Thank you for the details!
It is possible of course. I logged in to quickly check your configuration, and the issue is caused by invisible generic filters. I removed them for your, it should be okay now: https://i.imgur.com/4uY5syu.png
Now only the selected custom fields will be searched and the items based on those fields will be returned.
If you also want to change what fields are displayed on the live results list – for example you want to display the custom fields there, then you can use the advanced title and content fields feature.