Herrenchiemsee (Prien Station ) ... [is] close enough so that you don't need to spend more than 2 hours of your day getting there and back on public transport.
Prien station, yes, not more than 2 hours, but Prien station is not Herrenchiemsee palace. It only take 55 minutes by regional train from Munich's Hbf to Prien Bhf, but the train gets there at 51 minutes after the hour. If you left Munich just before 9:00, you'll get to Prien station at 9:51. The next boat to the island is at 10:00, not enough time to get to the harbor by streetcar or on foot. The next boat is at 10:30 and takes 15 minutes to the island pier, from which it is a 16 minute walk or carriage ride to the palace. So from Prien Bhf to the palace takes 1:10; it takes 2:05 from Munich Hbf to the palace - one way.
If you have a tour reservation, you have to pick it up from the kiosk next to the pier when you arrive, 45 minutes before the tour. Figuring a wait in the line at the kiosk ('cause the boat just arrived with lots of people with reservations), the tour will start one hour from your arrival on the island and runs 30 minutes. With the walk back to the pier, you'll only be able to catch the boat that leaves 2 hours after your arrival. You'll still spend almost 1½ hr at the palace for the 30 minute tour.
If you go without a reservation, like I did, you might get lucky, like I did, and get a tour within a ½ hour of arriving at the palace, and be able to get back in time to catch the boat a half hour earlier. Still you'll be at the palace for an hour. ( Actually, I stayed longer at the palace, because it was around noon, and I had lunch there.) But if you don't have a reservation, and it's crowded, you might wait more than an hour for a tour.
The trip back to Munich, considering the timing of the boat and train will take at least 2:40 from when you leave the palace, so, with a reservation, you'll spend over 6 hours, 4¾ hours of it traveling back and forth, for a 30 minute tour of a poor copy of the real palace at Versailles.
If you are on the way from Munich to Salzburg, as I was, it won't be so bad - a four hour (min.) stop over to see the palace, but as a day trip from Munich, no.