Huh? You can animate the values in Unity. At least as far as I know. :o
As can be seen here:
The values I animate are the Distortion_Strength, the Global_Speed and the VertexOffset_Strength. I don't recommend using a global speed multiplier since it kinda doesn't work as expected, but in my case, since it gets all hectic, it's fine.
As explained in the small video, I simply take the result of my panning textures and feed that to my vertex offset output, after multiplying it by the value I will then animate.
If you want the complete shader, here it is:
it isn't optimised at all and still has some remnants of an older shader of mine that I took as starting point (mostly distortion and depth, that I don't really use in this case).
And also, as you can see there, I use the Alpha channel of the vertex colors a bit everywhere.