Not sure, it’s trial and error.
Changing the buffer size on Kontakt has any impact?
I know that after loading an instrument on Kontakt your disks out of the game and it is loaded in RAM, so no SSD problem here. That if DFD is not selected (little wrench icon on top left of kontakt instrument). If it is try changing this to “sampler”.
I 've seen this topic recently. Maybe you can try disabling the ASIO Guard just for Kontakt in “VST Plug-in Manager” and see what happens.