How to save a file quickly and no need to wait for the external hard drives to "wake up"?
The save button is checking all mounted drives, and will spin them up.  

Your only way I can think of to do this is to prepare a couple of scripts.

See the man page for diskutil.  If the mount point (diskname) is BigFatDisk

then to unmount the disk it would be something like

diskutil unmount BigFatDisk

Now to keep everything sync'd to BFD you would run a script now and then

diskutil mount BigFatDisk
rsync flags local disk BFD
diskutil unmount BigFatDisk

A second option is to replace the disks in the BFD enclosure with hybrid disks.  These have an SSD chunk and a spinning rust chunk, and are ideally suited for this.

A third option is to let your disks spin whenever the machine is awake?  The amount of power they use is small, and increasingly MTBF times are being given as X spinups, not X hours.  A hard drive 2 years ago used 5-7 watts.  I'm sure it's better now.  So let's use 5.  That works out to 40 kWhr per year, roughly.  At 15 c per kWh that's 6 bucks/year.  Seems to me that this is pretty cheap compared to the hassles you have now.

I have set my computer to turn the screens off after 20 minutes idle time, but never to turn off the CPU or spin the drives down.