I think you may be dealing with MNSSHP about that time too...but if they close early for Night of Joy there may be some waiting for a day that it doesn't close early.
We have gone to the Magic Kingdom during the Saturday Night of Joy twice. It will both be very empty and fairly crowded the same day.
Attractions are virtually a walk on first thing in the morning with very low crowds. Most of the morning is this way. You will get a lot done if you are there by opening.
People with Night of Joy tickets can enter the park starting at 4 PM, so it will get very crowded from 4:30PM until close at 7 PM.
My suggestions:
If going to MK that day but not the Night of Joy, get there at opening and stay till 3:30 or 4 PM
If you are going to MK and the night of Joy, get there at opening and stay the morning. Then head back to your resort to rest for the Night of Joy. We get back just before 7 PM. If you spend most of the evening watching performers, you will stand quite a lot and that afternoon rest will help out.
In our 2014 trip I broke away from the performers to see what the crowds at the attractions are like later in the evening. Generally short wait for most rides. You can read about it in my trip report at http://www.bochnik.com/disneysept2014/disneysept2014.htm
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