[MA Softball Ump]

Serg has it right. Just to make sure all has been clarified, in ASA:

"Just to verify that we are on the same page, based on the fact that the definition of leaving the box requires one or both feet to be completely out of the batters box, then in the situation below the batter would NOT be out."

Yes, one or both must be completely out of the box (outside the line)

"B1 starts out with both feet inside the batters box. He then places his front foot so that some portion but not all is outside the batters box without requesting time. Has he left the batters box? NO, he has not left the box."

You are correct.

"He then replaces his front foot in the box and hits the pitch. Time was never granted. Do we have an out? NO OUT!"

Correct, his foot never entirely left the box.

Did this help??

TJ