Sprouting is very dependent on temperature, the age of the seed, the species, and likely things that otherwise would only affect the flavour of pizza.
I would suggest something like this:
Get a series of pails. Make screen lids for them. (Take the regular lid, cut an 8" hole in it. Stick on 1/8 screen wire using silicon seal)
Put grain in the bucket. Soak for X minutes. Invert the bucket to drain.
Twice a day fill and drain the bucket. This is all just standard sprouting.
The buckets take up less room than trays, and you don't need the trays until the seeds sprout.
One you start to see sprouts, transfer the seeds to trays, and put in light. Again, you will need an easy way to fill and drain. A simple way is to put a hole in the bottom of the tray, and stuff it with a chunk of sponge. Add water to the tray. The water will slowly drain through the sponge. The size of the hole and how tight you pack the sponge controls the drip rate. This water may have nutrients for your livestock. A sponge is far less likely to block. A hole small enough to give soaking time will block with the first loose floaty that comes along.
Look into self starting syphons. Try on the marijuana hydroponic web pages.
As to optimum time -- that's tricky. My thought: When the sead leaves look ready to fall off the plant has converted most of the seed mass into young plant, but the amount of simple celluose is still at a minimum. Better than this would require nutrient testing