I'm not up for replying to my own posts, but I can't think of a better way to bump this up a bit and maybe get an answer.
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I'm assuming that you are talking about the distortion and vertical break up of the characters. One option is Card Dance. Probably a separate layer for every letter, and some distortion maps. It would take a bit of fiddling around but that's where I would start. 50% gray does not move the rows or columns so something like this would get you started. All modified properties of card dance are revealed. It will take a bit of time to wrap your head around how it works, but I think I could pretty well duplicate this logo transition using a separate text layer for each letter.
You can turn off the gradient layer and it will still work.
Thank you so much, Rick! I'll try it out as soon as I get to that laptop again