Trying to assess what I may be doing wrong.  I have tried different margins, scales, positions, and shapes of the capsule (box, sphere, and capsule).
Pics show sequence of animation, hair continuously breaks through bounding line as if bounding shape is not there.  Also tweaked on and off Hair set (checked) to collide...Perhaps bug?
Any thoughts appreciated, thx!

Have you tried adjusting your weight map on the hair in the upper region. Reduce the Movement closer to the crown am make it play a bit nicer with the cage. I struggled with a long hair setup for a while. Most of what you have tried is what I did. Reducing the cage size and using a bit more margin is what worked on upper part and the Weigh map. 

Hi Paul, thanks for your suggestions!  I very much appreciate it.  I actually had come to the similar conclusion that I needed to scrap the whole bounding box testing and just go with tweaking the weight maps.  That seemed to be a better option, no matter how much I changed it just didn't want to abide to the bounding box.  I next tried your suggestions, but they didn't seem to change anything.  It was a Daz hair imported in, but with soft cloth physics enabled, so I don't know but maybe the in-iClone hairs have something else going on that makes them work better?

In any event, here is what I achieved just with weight mapping alone... You can see the clipping on the lower left jaw (the figure's right side chin).  
I guess I can put in a Feedback ticket to see if we could get true bounding box usability, would love to have full blown control...
Get it...GET IT!?

Mehh....Anyway.      

Yes full blown control would be good. I know your pain trying to work with the collision cages. Either you get poke through or set to high it's like having static hair where the hair repels. I uses a post process which get me a good result until Iclone manages to get better control on the collision shapes. let me know if you past a feedback track and I will put in a vote on it...