I ended up using the HSB to RGB conversion algorithm found at http://www.adafruit.com/blog/2012/03/14/constant-brightness-hsb-to-rgb-algorithm/, I adopted the inital (long) version. Perhaps this can be further optimized but for my purpose this was perfect!
As the hsb2rgb method is in C and I needed C#, I'm sharing my version here:
    private byte[] hsb2rgb(int index, byte sat, byte bright)
    {
        int r_temp, g_temp, b_temp;
        byte index_mod;
        byte inverse_sat = (byte)(sat ^ 255);
        index = index % 768;
        index_mod = (byte)(index % 256);
        if (index < 256)
        {
            r_temp = index_mod ^ 255;
            g_temp = index_mod;
            b_temp = 0;
        }
        else if (index < 512)
        {
            r_temp = 0;
            g_temp = index_mod ^ 255;
            b_temp = index_mod;
        }
        else if ( index < 768)
        {
            r_temp = index_mod;
            g_temp = 0;
            b_temp = index_mod ^ 255;
        }
        else
        {
            r_temp = 0;
            g_temp = 0;
            b_temp = 0;
        }
        r_temp = ((r_temp * sat) / 255) + inverse_sat;
        g_temp = ((g_temp * sat) / 255) + inverse_sat;
        b_temp = ((b_temp * sat) / 255) + inverse_sat;
        r_temp = (r_temp * bright) / 255;
        g_temp = (g_temp * bright) / 255;
        b_temp = (b_temp * bright) / 255;
        byte[] color = new byte[3];
        color[0]    = (byte)r_temp;
        color[1]    = (byte)g_temp;
        color[2]    = (byte)b_temp;
        return color;
    }
To call it based on the code linked in the original post I needed to make some minor modifications:
    private byte[] SmoothColors1(int maxIterationCount, ref Complex z, int iteration)
    {
        double smoothcolor = iteration + 1 - Math.Log(Math.Log(z.Magnitude)) / Math.Log(2);
        byte[] color = hsb2rgb((int)(10 * smoothcolor), (byte)(255 * 0.6f), (byte)(255 * 1.0f));
        if (iteration >= maxIterationCount)
        {
            // Make sure the core is black
            color[0] = 0;
            color[1] = 0;
            color[2] = 0;
        }
        return color;
    }