I found the problem to this issue. I have my 'system' share set to cache only, but some data was still on the array. I moved it all to the cache with the 'unbalance' plug in. Now the containers don't become unresponsive anymore when the array goes to shit. The reason i'm still here talking about something that has nothing to do with the mover is that my problem is exactly the same as the original post.
The first 5 mins of the import makes the whole array unresponsive, meaning that nothing can be read from it. After 5 mins I gain access to it again but it is
noticeably slower (kinda expected). After some time it goes back up to 100% CPU and nothing can be done, until it is done.
You said this is probably because of slow drives. I've excluded that one drive that contains all the data, forcing unRAID to write to the next one. Plex still can't play the media that is on the "idle" drive.