Thanks to Lady Marguerite, and the trading of dye-stuffs, I was able to get my hands on a small amount of fresh buckthorn berries (rather than the dried ones I had used for my first green dye experiments). So, last week I did my experiment.
I basically did the same process as the previous dyes so I could do a proper compare. The only difference is that I didn't need to soak them overnight to reconstitute them. I also shortened the cooking time a notch (down to about seven minutes instead of ten).
The berries themselves were pretty purple when I squished them, so I had my doubts it was going to work. And even when I was cooking them it didn't look all that green, but it definitely worked.
The picture below shows the different samples. The two on the right are my original samples and the on eon the bottom left is the new one. It's much more green, and doesn't have the yellow highlights that the other two have.
I wonder if the reason for the colour difference is the ripeness of the berries. If the fresh ones were more ripe they may not have had as much yellow pigment in them (given that the unripe berries are used for yellow dyes).