Hi,
Bad news is: You can’t do it with those plugins.
The closest I think you can get is with a “CC Bulge” Effect, combined with a circular mask.
Animate the bulge down from 1 to 0 while you interpolate the mask from circle to the full layer.
Unfortunately. Bulge is not a true Spherize distortion, but it might come close enough for your project.
(To my taste the Spherize-filter doesn’t actually look like a sphere either, though CC Sphere nails it)
for a true unwrapping effect, you’ll need a 3d program. I know Cinema 4D can do it easily.
As for 3rd party plugins:
I’m not sure if this effect can be accomplished with 3d invigorator.
But Forge.net’s Freeform might do the trick.