Hi!
Thanks for the details, it helps a lot.
The answer is yes, you can achieve something similar. To save you some time, I recommend checking this video tutorial.
While it’s for a WooCommerce setup, it does not matter, it works the same way for any other custom post type.
I think it’s covered in the video as well, but you can use the settings and the search results shortcodes to move the live results to a different position.