How can I achieve the visual of objects pressing against membranes more beautifully? Source files here and here.

Hey folks. Currently building a project for a client which involves shapes and creatures pressing and moving against a membrane. I've tried using shrink wrap, cloth simulations and blend shapes to achieve the effect, but nothing seems to give me the same freedom of movement as rendering a depth pass sequence of the objects moving and using that to drive a displacement modifier.

Unfortunately, it's still a bit rough. Objects extruding far out of the surface look stretched and glitchy with narrow triangles. Additionally, the mesh is using 64,800 triangles, which is about the maximum I can use in Unity Realtime per object.

Can anybody think of a prettier / more efficient way to achieve this effect?
While I was ultimately forced to use a realtime displacement shader in Unity to achieve the effect and my client later moved onto an off-the-shelf raymarching solution in Unity, I was able to slightly improve my workflow in Blender.

Using a Displacement Modifier to initially perturb the subdivided plane provided a gentle organic 'texture', I then followed this with a Warp modifier to move the vertices in the direction of my depth map (the Warp modifier obviated the need to worry about normals as it extends the vertices towards the 'to' empty).

While not perfect (still getting stretching artifacts, etc), it worked out pretty well within Blender and I was able to export Alembic bakes for playback in Unity.