How to free-form transform/distort image?

Hello, everyone!
I need to fit my photo on a video of a hand-held piece of paper that is a little distorted by holding in fingers and moving.
I tracked it using planar tracker (Mocha Pro) and exported into Motion, so now I have 4-corner pinned rectangle in different layer, matching movement of 4 corners of this paper piece for all length of clip.
BUT, as paper is not just 4 cornered (but has some push distortion, imagine you hold a soft piece of paper in hand), just matching movement of this rectangle won't help, I think I need to free-form distort some parts of my photo to perfectly fit in my final render.
Is it possible to do such a simple thing? I surfed all internet, but didn't find an answer (everywhere is a TV Screen, or plain sheet of paper replacement that have just 4 corners with no distortion). All i found is just a CHV Deform FX plugin, but it costs some money, and I don't believe Motion doesn't have this function itself. Or there's another way of solving a problem?
If you don't understand what i mean, just let me know, I'll upload a video or photos to show it.
Thanks everyone who will help me, I'm f*ing about 3 days about this and even can't sleep thinking of solution...

hi,
motion can't do this kind of mesh deformation on its own. I believe the chv plugin does have this kind of thing, but I don't know how useful it is. The only solutions I can think of are hopelessly time consuming and wouldnt look convincing.
adam

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