Min of Positive Values

Per your file:

A3: =INDEX($C$6:$K$6,MATCH($E$3,$D$27:$K$27,0))

Do not use Merged Cells -- for Horizontal ranges you can use "Centre Across Selection" to get the same effect without any of the associated headaches.

On an aside the SMALL(...,COUNTIF()+1) approach is certainly one I would opt for in preference to a MIN array regardless of Merged Cells issues.