Okay, I have made some progress. Starting now, when the search is indexing plants, it converts at that time the umlauted characters over to regular non-umlauted characters and then stores the result.
For example, as a consequence, if a plant is called Dornröschen then it will be stored inside the database as 'Dornroschen'. This way people can search for it using the non-umlauted character. The downside, though, is that it can not be searched using the umlauted character.
At this time, I can't see a way to have it both ways.
