It's my fault, you said inches. I can't believe someone at the FS would give you snow coverage in inches.
I came down Cajon Pass today and it appears there is still a lot of snow in the couloirs on the north side of Baldy. I was not far enough west to get a good look at B-P.
At 6 to 12" I would go. You could go in from Dawson Saddle with no exposure whatsoever, summit Throop, going up the northwest side of the peak, then onto Burnham and Badden-Powell. This way the kids at least get the initial peak and would be climbing the west side...the side least likely to have any snow at B-P. ACH seems to be open beyond Vincent Gulch, CalTrans no longer says it is closed on its website.