There is an error in the pattern for the Adult Large size in the set up round for the crown. You can’t go from 124 stitches around to 120 stitches around with only one decrease. Therefore, the set up round for the crown for the adult large size should actually be:

{k14, k2tog, PM} 4 times, {k15, PM} 4 times

That gives you 8 equal sections of 15 stitches each before beginning the crown decrease section of the pattern.

The hat seemed a bit deep, so I only did 7 repeats (instead of 9) of the two-row crown shaping and then I switched to knit only the second round (decrease round) of the crown shaping for the remainder of the crown until I had the correct number of stitches.