I cannot get their pink with plant based colors, this is why I said I think one of them is made with cochinneal. I do not use either Zn oxide or titanium dioxide.
Here is a picture with 100% plant based colors. I was aiming for purple, green and gold. I was trying to achieve the bright New Orleans Carnival colors so I used 100% coconut soap (20% SF so it is not drying). CO is so white that any color shows better with this single oil approach.
To get their shade of green I would simply use a little more annatto or beta carotene with my indigo. I get lime green this way all the time. I have other examples with a lime green if you want me to post the picture I can.
However, this backfired because customers think the colors are lab made, they are so bright and vivid. Nobody believes these are 'natural'.
The gold uses annatto and a little paprika, the green uses indigo and beta carotene, the purple is simply infused alkanet.