Index, Match. Reporting from skills matrix

Hi there,

I manage a team of instructors with a variety of competencies. I need to be able to manage their competencies to look for any shortfalls in my team.
I have their competencies in a skills matrix.
Please see the attached file where I've explained the situation and what I would like to happen. I'm really struggling with it, but I've made a little headway.

In K3 copied down
=IFERROR(INDEX($C$1:$H$1,AGGREGATE(15,6,(COLUMN($C$1:$H$1)-COLUMN($C$1)+1)/(($C$2:$H$5=3)*($A$2:$A$5=$K$2)),ROWS($A$3:$A3))),"")
and in N3 copied down
=IFERROR(INDEX($C$1:$H$1,AGGREGATE(15,6,(COLUMN($C$1:$H$1)-COLUMN($C$1)+1)/(($C$2:$H$5=2)*($A$2:$A$5=$K$2)),ROWS($A$3:$A3))),"")