Welcome to the forum, RJ.
"The absolute best thing to do is take the train and spend a night or two near the castles."
You may find this response unsatisfactory as well, but I happen to think it's the best tip you've gotten so far, RJ.
I hope you don't mistake Lee's "do the castles at Hohenschwanstein on your own" as an indication that you can just wander about Neuschwanstein's interior. It's a guided tour of less than 30 minutes. I think you get 35 at Hohenschwangau.
So... is the nearly 5-hour round trip by train and bus from Munich worth it? The reason there are so many rooms in the Füssen area is, in part, that some think the "castles" alone aren't worth the trip from Munich. The idea of staying over to enjoy the OTHER charms of this area as well is worth considering. Some research should bear this out.
This option may or may not apply to your situation of course. On this forum you will probably find that responses routinely stray from the parameters set forth by the OP. Your thread is no different. Remember that many others besides yourself will stumble into the forum to gather travel ideas and opinions from posts like yours - and that the regulars here post stuff which might not apply strictly to your situation, but may in fact help future readers on the general topic you brought up.
(btw - I love that portmanteau, Lee!)