...would it be better to leave Munich 5/16 and stay one night somewhere nearer to the castles, then continue on to Salzburg?...I’m also not super thrilled about adding more driving to the trip lol. Also we would then be doing these major tourist attractions on a Friday and/or Saturday so I could see it being much more crowded.
I share KD's take on the interior/tour of Neuschwanstein. Linderhof is more worthwhile. Extending a stay in Munich to do day trips sounds reasonable at first glance, but it is often problematic... many high-profile Bavarian destinations in RS's materials (Neuschwanstein, Linderhof, the Zugspitze for example) are simply too far away and very inconvenient as round-trips from Munich. So yes, I think your new idea is better.
But it's still not a great plan, as you seem to realize. So my question is whether you have given consideration to the alternatives... You can quench your thirst for palaces far more easily in...
Munich (Nymphenburg Palace), where King Ludwig II spent his childhood and was coronated. Much more to see here than at Neuschwanstein. Wonderful place. No day trip required at all.
Prien (Herrenchiemsee Palace), Ludwig's most impressive palace of all IMO, on an island in Lake Chiemsee with the Alps as a backdrop. Direct train from Munich to Prien = 1 hour. Then you shuttle to the dock for a short ferry crossing. You can do Herrenchiemsee as a day trip from Munich, OR you can do it on the way to Salzburg, as Prien lies directly on the Munich > Salzburg railway. Prien station has lockers for your bags.
Personally, I would streamline this stay and split my nights between Munich and Salzburg, probably 3/4 or 4/3. And from SALZBURG, I would take a day trip into the mountains. Berchtesgaden (Germany) is a great - and easy - day trip from Salzburg. Bus 840 gets you there in less than an hour. The same bus will drop you at the Koenigssee (lake) or at the base of the Jennerbahn lift.
Bus 840 schedule: https://www.koenigssee.de/cdn/uploads/840.pdf
Another day trip or half-day trip from Salzburg might be Hohenwerfen Castle, in Werfen (Austria,) a genuine fortress from the Middle Ages - with a falconry exhibition - that is only 40 minutes from Salzburg by direct train.