I think you got it mostly right, except the Dutch part. I doubt they'd pick a side even if French and British troops move through Belgium, they'd only pick a side if they got invaded. The dutch were quite attached to their colonies and a war against Britain would mean the loss of those. They'd try to avoid that if at all possible.
Whereas that's true, the question is whether the Dutch would believe that the Allies stop on the Dutch border. I wouldn't believe that.
Second, question is what the Belgian army would do. They have to retreat, and probably they'd try to retreat into Germany. Best way to do that: cross the Netherlands, already suspecting an aLlied attack on themselves...
I agree that the Netherlands do not want war, but I believe that the Allied invasion of Belgium would start a chain reaction which would end in the Netherlands joining the Germans and an endless (and fruitless) discussion after war whether this was intended or not from either side.
Anyway, the main point starting the discussion was whether Germany is in a better strategic situation with Austria-Hungary in the Allied side. Now considernig the options:
1. defensive stand against the French. Good strategic situation: Defenses in the Vosges mountains, ultimate second defense line on the Rhine. Should provide enough time to destroy AH.
2. France and Britain invade Belgium. Pretty much the same situation as in 1. German frontline in the West increased by 60 km in the Eifel mountains. The Netherlands are unhappy, so are the US. Probably the Germans advance into Belgium, securing Luxemburg and Liege, a good defensive position in the Ardennes and along the Meuse, and at least some Belgian troops helping them. Should provide enough time to destroy AH.
3. France and Britain invade the whole Benelux area. The Germans advance, probably halting the Allies along teh Meuse-Rhine line, securing a good defensive position, local support, the Dutch fleet, probably most of the Dutch army and parts of the Belgian army. Should provide enough time to destroy AH.
Now once AH is completely occupied, the Germans can turn West with the help of the Russians and their food situation as well as supply with raw materials secured.
A main point is also that with France AND Austria-Hungary on one side, Italy should definitely be on the other side. This should distract quite a lot of troops from the Allied side into the Alpes. Question is whether France then wants to enlarge its front line at all.