Warning: Long post, several interrelated issues …
I recently moved my library contents to an external SSD drive as suggested. After the move, I set the content location in the file management section of Native Access to the new location and then opened the library view with "All" selected. As expected, the instruments showed a "Repair" button. I chose the Repair All function, changing the content location to its new value, and after a few minutes, all instruments were successfully repaired. I checked a few of the installation paths and everything looked OK.
When I now open Kontakt 8 Player's library view, however, about half of the instruments show a plain grey file folder instead of the appropriate icon, and Electric Keys - Phoenix appears twice in the grid, once with its normal icon and instrument name and once as a grey folder labeled "Electric Keys - Phoenix Library".
When I click on any instrument other than Piano Uno or Electric Keys-Phoenix, each preset is listed twice. Clicking on the first occurrence in each preset pair produces a "File not found" error message, but the second listing of the same preset behaves normally. Clicking on the ">" symbol in the upper right corner of any icon or folder in the library view other than Piano Uno or Phoenix also produces the "File not found" error. Reinstalling the problem instruments changes nothing, even when preceded by an uninstall.
When I open the library view in Kontakt 7 Player, aside from the grey folders issue described above, all else appears and works as expected. Returning to Player 8, all of the problems previously described are still there.
I think I could probably resolve the cited issues by removing every trace of NI apps and content from my system and reloading everything with all content sent to the external drive initially, but I'm hoping someone here may have a less drastic fix.