Double hung sash window, any way to prevent the top from being moved down

These windows must have been installed into window casements that were built in place or reused from previous windows. The reason I comment about that is that if the windows were new units with the windows themselves pre-hung in the casements it is hard to believe that they would have the misfit that you describe as delivered from the factory.

In any case you would do well to see if you can talk one or two other contractors to come out to look at the installation to see what feedback they would give to you.

Sounds to me like you need to argue the case for a replacement set of new windows. If by chance you have not paid for the job you should withhold such payment until the problem is corrected to your satisfaction. If you have already paid then you have lost a certain amount of leverage but threat of a civil suit may be in order if you do not get a suitable response from the contractor. Of course you have to weigh the cost of getting involved in litigation against the size of investment already made in the windows.

Many air conditioners have a "fresh air" setting; at that setting, they blow air from outdoors into the house. Although it does cost electricity, it's better than opening the window because it moves are even on dead-still days.