Colorizing an image with three colors - one being white while maintaining shadows/highlights

Hi guys -

I have a background image of wood - barrel staves to be exact which I am trying to "colorize" with the colors

of the Irish flag - Green, White, and Orange. My approach to doing this was to use the hue/saturation feature

with colorize checked. While this works to a point, I am finding the results are sub-optimal, particularly with the white portion.

The white looks more like a foggy overlay than actually turning the wood white - while maintaining the definition that I need.

Does anyone have any suggestions about how to get the result I am after?

Thank you,

L