Hi,
This sounds like an odd suggestion ......
If you're an atmosphere sort of person ...... my tip is to hang back and try and (without bringing attention to yourself) try and be the last person leaving each room and then when everyone has left, steal surreptitously back to the previous room for a moment or two. The groups can be a bit of a bustle with all the jabbering and everything. The main (music?) room at the top which looks out through the colonnades to the surrounding countryside is particularly atmospheric and a few moments in this wonderful room by yourself will be memorable.
Remember that the castle is still brand new as Ludwig didn't occupy it properly before his untimely "death". So it's a stunning experience.
Enjoy your visit.