First things first, don't sweat /dev/shm.
Second, I would ask "What benefit would doing all this work have?".
Do you have a 'standard' filesystem structure for all your servers?
Is there a need
to keep everything on this server? (or can you flatten and reload it?)
What happens if this server "breaks"?
Are there users that will notice.
Will you lose money due to the downtime?
You also mentioned something rather odd....
using a GParted Live CD, not really an option for me, as is reinstalling the OS and redoing the partitions (which I would if I could)
It kind of sounds like you cannot afford to bring down the system...and doing something as drastic as resizing the main partition, using LVM, and/or replacing important filesystems (like /var) are absolutely out of the question for you.
need to bring this system down if you want to change the partition & filesystem layout.