Well the system seem pretty straightforward, in the breakout the spreadsheet and day-planner kind of way.

i think if you do a moon check lore, you should get a little buff icon come up for the time remain in the day or the moon phase, The little icon should show you the moon phase graphically, and it's tool tip should tell you fancy name of the phase and the quarter one. This would help with mushroom farming.

However;
If there is some trick to using 12 HR (etc) boxes, using them for multiply crops, I sure can't figure that out. You seed a 2 hr crop, come back right when it is done and your option is to retire the box. You close the dialog without clicking retire, it still despawns as soon as the dialog window closes.