Bill - I think you have already solved the problem. Using grayed down and less saturated versions of the green works well.

You're dealing with an animal shelter not a fashion line. The colors should be soft and friendly. Maybe some tweaking but in my opinion as the ancient author of Looking Good in Color, (1995! https://www.amazon.com/Looking-Good-...s=books&sr=1-1) I like how you have handled this color.