I know tar should have no problem backing up a whole system's pile of Gbs certainly under a powerful spec'd PC.
Even with plenty space, one big file is somewhat unwieldy. I would tend to do each directory and then it's simpler if you only need to restore from that.
I notice you exclude certain dirs from the big file but do you do them seperately?
I ask because when I do backup it's not from the booted hdd so I see that some of those supposedly self-refreshers still have sub-dirs, so I back them all up.
I do this. with my cursor being at the root of the hdd being backed up.
NB. (leaving out compression and backup medium for clarity)
tar --no-recursion -cvf basedirs.tar * gives me the whole dir base structure and any files in the / root dir.
tar -cvf bsbin.tar bin
tar -cvf bsetc.tar etc
and continuing on down, usually breaking up /usr into 3 seperates.
Makes lfe less complex for me anyway.