Let's set aside the biting of people who come into your house with out proper notice (as I think that is justified). (No, I do not allow my dogs to bite people, I am just saying it is a reasonable reaction.)
Fear biting is very hard to fix with out lots of time spent training, etc. It sounds like investing that time is not an option (and no, that is not a dig, it is a fact for very many people).
If he is so stressed that he bites the livestock he should in theory be protecting it seems like putting him down might actually be a gift.
I agree that the unannounced "intruder" was justifiable. There have been two other minor biting incidents with him on our property, plus his attack on the sheep.
We do not use him to guard our livestock. As a rule we keep him well away from the sheep, goats and horses. It was a fluke that the ewe walked over to where he was tied up the other day.
ETA: It can be quite exhausting monitoring him constantly. "Where's Chui?" "Is anyone coming to the farm today?" "Does he have his muzzle on?" "Why are the dogs barking? Is Chui in the house or in the kennel?" It's emotionally draining too, always feeling worried and on-edge about keeping him under wraps.
I can't imagine how much time it would take to work through fear biting. Also, since it is combined with a natural instinct to guard and protect, I don't know if it could ever be worked out. Even if we did somehow get him past his immediate biting reaction in a controlled environment, I'd never feel secure to trust that training. What little thing could someday trigger the same response? Especially since it's a well-ingrained behaviour now, in a 7 year old dog.
Being at the point of even considering destroying him is a big deal for me, as I never would have been able to even think about it a few years ago. Even now it makes me truly upset, as I love my big dog.
But not all decisions can or should be based on emotions.