Basically I want my footage to do this:
...And I'm not sure of how to go about it in AE. Any ideas would be really helpful.
If it's too difficult to simulate, then perhaps a way of causing that glitch so that I can capture it?
There are some effects presets called Bad TV. I think there are 3 of them. You can search for them in the Effects and Presets panel. That should get you started. From there you could add another copy with mosaic, card dance, or other effects to build up the effect. There is no one click one plug-in solution to exactly duplicate that playback glitch.
The best way to simulate a playback glitch is to do it. It's fun, too. REcord yor move to VHS tape and mess with the tape.