With a long enough runway and the right weight, etc., V1
could be after Vr. It doesn't happen often but it could. Therefore if it didn't fly at Vr, an abort would still be feasible. It's when V1 comes before Vr that you are committed at V1.
Also, if you make an intersection takeoff and you've computed V1 using the full length of the runway, then the computed V1 is no longer valid. It's something smaller.
G+
The court would understand because you were following company SOP's.
I wouldn't bet on it. Lawyers don't think that way. They would simply say the SOP created a dangerous situation and continue the lawsuit.
Intersection takeoffs mean you've negated some of your safety margin. If you choose to make one and you have an accident, you have put yourself in jeopardy for not choosing the safest course of action. Following SOP might help you keep your job with the company but won't help in a lawsuit.