For the record, here is the script used to remaster Debian Live 9.1.0. Basically, it performs the aufs union mount, copies the whole thing to a directory with rsync, and then compresses the result. Squashfs-tools are needed. The whole operation takes only a few minutes on a contemporary i7 machine with SSD disk.

[ -d sqfs ] || mkdir sqfs ;
[ -d persfs ] || mkdir persfs
[ -d aufs ] || mkdir aufs
[ -d copyfs ] || mkdir copyfs

# Running under Knoppix 7.7.1 w/Debian 9.1 image on same partition as Knoppix, persistent store at /dev/sda9
[ -d /media/sda9/deb91_1p ] || mount /media/sda9
fsck.ext3 -y /media/sda9/deb91_1p/persistence
mount -o ro,loop /mnt-system/deb910/live/filesystem.squashfs sqfs 
mount -o loop /media/sda9/deb91_1p/persistence persfs

mount -t aufs -o "br=persfs/rw=rw:sqfs=ro,noplink" none aufs 
# Clean up, in case
rm -rf copyfs/*
# Copy union file system
rsync -axu aufs/* copyfs 
# Clean up mounts
umount aufs
umount sqfs
umount persfs

# Compress file system to new live file 
mksquashfs copyfs filesystem_rem_1.squashfs
Afterwards, the new live file is copied to a new directory, a new persistence file is created in a new directory, and a new grub entry is created with the new locations. This way, it is possible to go back to an earlier version on the fly if somethings goes very wrong. At irregular intervals, depending on how much is changed, the new persistence file is backed up.