Running a Brownian motion of randomly radius changing particles

Dear LAMMPS Users,
I have been working on Brownian motion in LAMMPS for a while now. For a particular simulation problem, I wondered if there is a way to simulate spherical particles with a randomly changing radius during the simulation run.
With previous discussion and help from the mailing list, I have tried running this simulation with a fix adapt. Still, somehow it only grows or shrinks the particle radii uniformly during the run, and this fix works on the entirety of the group all at once. So if I am increasing the size, say from 1 to 1.2 A over a course of 10000 simulation steps, all the atoms within the group undergo this transformation at the same rate.

This is rather tricky business, since for a condensed system you can only make small incremental changes or else the simulation will diverge and crash.

Fix adapt only supports equal style variables. You could try to extend the code to also support atom style variables, but that variable would have to be programmed in a special way so it will only create small incremental changes toward a random target.

The alternative would be to try and do this with LAMMPS (or Python) scripting by breaking down your simulation into many small chunks using a loop and then changing the radius parameter randomly by small increments or incrementally toward a set of randomized target radii via atom style variables.