Went from weird to really weird. I factory wiped and flashed stock+tweaked and got the same problem on a fresh system. As an experiment, I then flashed just the old data partition with the same problem. So, it doesn't matter if it's clean or dirty, if it's stock AQF5 or stock+tweaked, I have the problem.
But, I do have a little better definition of the problem. It's more audio than video. And only with the tablet speakers, not Bluetooth. If I turn on Bluetooth, both audio and video play perfectly fine. Without Bluetooth, there's no audio and the video stutters (to better describe, the video plays at just a few frames per second and occasionally jumps back by a few seconds). Doesn't matter whether the source is on internal or external sd; didn't matter which of several video or audio players I use.
EDIT: One more data point. I booted into SAFE mode and it still stutters. I can turn on Bluetooth in the middle of a video or mp3/wav audio, the player will correct itself and be perfect.