I think sharing /proc and /sys is a bad idea. Sharing system directories rw would be a bad idea for security reasons. Look at the Filesystem Hierarchy Standard. You can mount the static partitions read-only. Since they don't change, you only need to back them up once. The /proc, /sys, /dev, /tmp, /var/tmp/ directories don't need to be backed up. /proc & /sys are psuedo directories, containing psuedo files that don't exist until being read. They are created on the fly. One item in /proc will read the entire memory space. The device nodes in /dev are created when the system boots.
It may be better to mount the destination of the backup and back up the files from the RH 8 machine to the share.
If it is OK to power down the RH 8 host, backing up from a live disk, so the filesystem is off line will allow a more accurate backup. You could create image dumps this way, which could allow a quicker restore in case of drive failure. But I'd still recommend file backups for this application's data files.