tickets to Neuschwanstein must be picked up at least 90 minutes before the start time
That was one of my concerns. That only leaves you with 60 minutes to take a 40 minute tour (assuming they give you a tour time exactly 90 minutes after your expected arrival time), and return to the parking lot in Hohenschwangau. Actually, you had better make it at least 100 minutes after your anticipated arrival time, since it will take time to find a parking spot, walk to the ticket kiosk, and possible wait a few minutes in line (although when I picked up tickets, there was no line).
But the bigger problem, as I see it, is that you have 4½ hours of sightseeing and over 2 hours of car travel before you need to arrive at precisely the correct time to pick up your tickets for Neuschwanstein. What could possibly go wrong with that?
It might be better to start with Neuschwanstein, so you could better predict your time of arrival, then to Ehrenburg, Linderhof, and Ettal in that order. I would rate Ettal as the least interesting of your destinations, and it could be omitted if you run late. Even then, you had better leave some leeway for arrival at the Hohenschwangau kiosk to account for a delay in getting the rental car or traffic delays on the way.
Assuming you are planning to eat breakfast before you pick up the car, your schedule has no time to stop for lunch. Are you really going to go almost 12 hours without eating. Well you have 90 minutes between the time you pick up your tickets and the tour time, and it only takes about 45 minutes to get up to the castle, so you would have time to grab a brat on a roll at the Schlossrestaurant just below the castle, but by then it will be after 3 PM.
The walk from the parking lot to the ticket kiosk at Linderhof is short as is the tour of the palace itself, but the grounds should not be missed. When I was there in 2007, I spent about 5 - 6 hours exploring the whole place (and lunch). I had planned to go to Ettal on my way back to Oberammergau, but I spent longer at Linderhof than I had planned, and it was my first full day in Germany, and I was badly jetlagged, so I went directly back to Oberammergau. I had previously researched Ettal and didn't really find much of interest, so I chose getting back to my room over Ettal.