Generally combining multiple search/exclusions plugins may not work with each other – one may not pick up exclusions from others, it is not possible to design them like that.
You can exclude the same items within ajax search pro too, via the exclusion options. They will not show up afterwards.
There is also an issue within all of the page and ajax requests – I see a custom code injected to each request, as you can see here: https://i.imgur.com/eP4O8lV.png
It is directly printed into every output – it is probably an incorrectly added as a custom code somewhere. I strongly recommend checking and removing that, it will have an impact on your overall site performance.
I checked the configuration, and the index table engine was not enabled. After turning it on, the pefromance greatly improved from around 7 seconds to a 2 second response time. That seems to be very nice given the overall page responses and generic ajax response are around 10 seconds.