I'm posting your message to the LAMMPS mail list, as
others may wish to comment. You could do something
like a capped LJ potential by using fix dt/reset which will
not let large forces blow atoms out. But soft potentials
work better for overlapping polymers.
You'll have to contact Barrat, et al directly for details
on their method. Re: chain growth, some people have
added their own stuff to LAMMPS to do this, but
nothing has made it into the mail release.