Lattice control of multiple objects without distortion

Question

what i am doing
: I am looking for a simple way to animate a cobblestone floor ripping apart in a specific and easily controllable way. I currently have broken down the floor into segments, each segment of bricks has a its own lattice which in turn is then linked to an overall lattice(animated with animall). seems to work fine, but its distorting the individual bricks a bit to much when I wish it could just increase the spacing between the brick for a more realistic look.
research
: I found one example where a parent object is made for each cobble and then using the "child of" constraint  to attach them to a vertex group. this kinda worked, but i could not get them rotate properly as to maintain their alignment to each other.
question
: what can i do to get a lattice type control of multiple cobbles without distortion?
side question
: am i going about this all wrong?

I would really appreciate any insight given.
edit:
test file https://gofile.io/d/powzGI

Robin Betts · Answer

One approach would be to use vertex parenting.
Create a mesh containing triangular faces which are unambiguously closest to their corresponding cobblestones. You could create the cobblestones from the mesh before triangulation, (as I did here,)  or the other way round: create the mesh from a duplicate of the bottom faces of existing cobblestones. The mesh faces don't have to be connected to one another, in fact, it would be better if they weren't.
Give the mesh Shape-Keys for the intact and torn states:

You have to plan ahead a bit; leave yourself  a state of the mesh from which you can parent the cobbles cleanly, or parent before making the shape-keys, if doing so can create the right parenting.
If they aren't already, P make the cobbles separate objects, and, all selected,  ShiftAltX, send all their origins to their individual geometry.
From there, with the deforming mesh in a matching state, and active, with all cobbles selected too, in Object Mode, CtrlP parent the cobbles to the mesh,  using Vertex (Triangle). The Cobbles will each be parented to the closest vertex-triangle in the mesh.
You are now free to deform the mesh's shape-keys, however you choose to, and the cobbles will follow, without distortion.

Here, with some Rigid Body cut in after the initial separation:

Lattice control of multiple objects without distortion

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