Henrik, thanks for the detailed responses. I did almost all of the permutations that you suggested last weekend. I left Video Quality at 20, but lowered "Images per second" to 5 FPS, played with the "Preset" slider, checked/unchecked Background Encoding, and changed the Decoding Library to Hardware. I did not try the Software_VLC setting though-- instead I changed it to Hardware while trying to fix the issue. I can play with that one tonight.
With Background Encoding checked, neither the AVI or MP4 have the issue, regardless of the other settings. The videos always play as expected.
With Background Encoding unchecked, the only setting that would alter whether the MP4's video would freeze is the "Preset" slider. "UltraFast", "VeryFast", and (I think) "Fast" worked ok-- no freeze issues. As soon as I went to "Medium", I experienced the issue on 100% of the MP4s.
I forgot to mention in my previous post, but I am using Win 10, and unfortunately haven't used NCS or iSpy on anything but Win 10, so I can't compare there. With "Medium" compression, the CPU definitely spikes up for each MP4. I will watch it tonight and see if it hits 100%.