I prefer Blender for this. Attach objects together, then create new empty texture and make it active "target" ( its node selected) in all materials ( drag and drop new texture from image pane to shader pane in each material) . Copy UV set and keep the original one with camera mark on while the new selected one with that…
It would be very simple to do this in a script. here's one I found on highend3d - it supports curve points https://www.highend3d.com/maya/script/randomize-points-for-maya