Even when you think you have them trained perfectly - they will still surprise you. You must be always vigilant even if you have spent years training your LGD type dog in obedience. The level of difficulty you may have is dependendent on the breed and the line within the breed. Natural working dogs will be more difficult to train and will naturally be less tractable. However, any dog can be trained to do what you want - just takes much more time and reinforecment with some. If you have the time and patience to invest you could train a good Kangal to do what you stated.
Just be aware of the difference between the hardware (dogs instinct and heritage) and the software (what you trained them to do). In a stressfull situation they may revert to hardware and thus endeth the peace and tranquility.
Give it a go ... good luck.