Return the Row Heading with Max Value in Table

I uploaded a simplified version of the workbook I'm manipulating for reference. I'm looking for a formula where I can get the ROW heading of a table to be returned based on the max value of a certain column. My column headings in the table are months. I have sepereate place in the workbook where I have the Months listed in a Column (A9:A......) and in Cells (B9:B....) I want to return the row heading name from the table. The tricky part is that the column headings don't always stay in same place, so Jan isn't always in A1, sometimes it is in B1 or C1 of the table.

Essentially from my months listed is seperate part of the workbook. In the cell next to each month I want to match that month with column in the table. In that column find the max value and return the row heading.

I've been trying some Index and Match formulas, but can't seem to figure it out to return right. Any help is appreciated.

Thanks so much, this is going to help me out so much!

Add it with IFERROR:

=IFERROR(INDEX($A$3:$A$6,MATCH(MAX(INDEX($B$3:$D$6,,MATCH(A9,$B$1:$D$1,0))),INDEX($B$3:$D$6,,MATCH(A9,$B$1:$D$1,0)),0)),"")

Thanks

Unfortunately, that didn't quite solve my issue. It is still pulling the first row heading, because techinally the formula isn't in error. There are just zeros right now.