The best I can figure right at this moment is to copy this formula into column M, and then copy past column M through column T:
=IF(A3=$K$3,COLUMN(A3),"")

Then in column V paste this formula:
=INDEX(A3:H3,1,MIN(M3:T3)+1)

That returns the correct answer but requires the use of those additional columns. I'm still thinking on a more elegant solution.