I just got off the phone with a Nikon repair tech supervisor. After explaining the problem I'm having (mirror locking up while seeing the shutter speed JUMP up to and flash at 1/4000" when it was supposed to be slower shutter speeds), he wants me to send mine in. No way. He understood completely and asked me to shoot in Manual Mode and Shutter Priority to see if my problem still continues.
Not sure if your problem is the same as mine, but if you continue to use your D750, keep watch of your shutter speed within the viewfinder. Once I realized what was happening, I have been able to thwart the mirror lock up problem. When starting to press the shutter (but BEFORE taking the image), I noticed the 1/4000" shutter speed flashing. Then I removed my finger from the shutter button without taking the photo, and the shutter speed would revert to normal.
All I'm saying is just keep an eye on it. It's hard to take a photo and not maintain attention to the subject, but that's what I've had to do.