Just some thoughts (take them for what you paid for them).
Don't "hibernate" the Mini.
Instead, when you're not using it, just let it sit there "awake, but idling".
The difference in power consumed between "sleeping" and "idling" is... well, next to nothing.
For the display, I'd first try setting up a hot corner to put the display to sleep (even though the Mini remains awake). You can do this in "desktop and screen saver", I believe.
No promises that this will work.
Another thing you could try:
As above, don't sleep the Mini, just let it idle.
When you're going to be away, reach forward and PHYSICALLY TURN OFF the display.
Turn it back on, when you come back.
Again, no promises.
I would shut everything down at night, and reboot in the morning.
Been doing this for 37 years with computers -- works for me.