How would I go about mimicking this halftone effect in GDI+?
It almost looks like Floyd–Steinberg dithered version of the image overlaying a full one but I’m not convinced.

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I gave this a try and got this result:

It may be a place to start. I did it like this:
matrix)
using a pattern mask (ie the dots)
I created the pattern mask like this:
And then I imposed it over the oversaturated bitmap using this technique.
Update: Elaboration on how the images got merged. Let’s talk even a little more general and say that we want to combine two different colorized versions of the same image using a pattern mask, resulting in a new image – we could do it like this:
Create THREE new bitmaps, all with the same size as the original image. Call them bmpA, bmpB and bmpMask.
transferOneARGBChannelFromOneBitmapToAnother method.
Done