Hi!
Thank you very much for the details.
I have looked at the front page, and I see you are using a custom shortcode to display in a two column layout, the search and the settings on the left, and the results on the right.
The problem is, that this shortcode is used on the page 2 times, and the first shortcode overlay is not in use (or at least I could not find the trigger). The second overlay when opens, the results are moved to the first overlay (invisible).
To resolve this, simply remove the shortcode from the first hidden overlay, and it should start working.
If you wish to use both overlays for some purpose, then I suggest making a duplicate of the search instance, so that it uses a different shortcode. Then using one shortcode in the first overlay, and the other shortcode in the second one.
I hope this helps!