Extracting Row And Column Header Coordinates From Value Search?

If the could be longer I would have included "when multiple cells can contain the same value"

I have a very large dataset that I would like to apply the following searches to, but I will include a smaller sample that gets at the point.

For example; in the following sheet:
Cat Dog Lizard
Red 1 2 3
Yellow 4 5 6
Green 7 8 1

If I search for "2", I would like to get back "Red" and "Dog". I was able (by looking at other posts) come up with a series of formula that allow me to obtain the sheet coordinates and convert them into column and row headers (using SUMPRODUCT Row/Column); however, when multiple cells contain the same value, the output becomes the sum of that coordinate and is no longer a reference to a specific header, so a search for "1" would not give me "Red" and "Cat". Ideally, if I searched for "1" I would get back "Red" & "Cat" as well as "Green" & "Lizard", but I would be satisfied with a formula that even just gave me back one of the two header pairs.

JordanSample Workbook.xlsx