BC, the sunlit soft summer sounds suspiciously like the Light summer palette from my color system. Light, Soft, and cool. My skin is also neutral to cool, my eyes are green, they can look light teal or grey depending on the light and what I wear. If my hair is a warm color my eyes can look olive green. My colors were very hard to pinpoint, and I ran through the color spectrum from Spring, autumn and summer. I passed well in all the colors because of my neutral skin and my eyes shift, but there were always a large group of colors in each of the previous palettes that didn't work for me. Mostly the very warmest of the colors. My natural hair color, which is hard to recall because I've used color for many years and now I'm grey, but I believe it's similar to yours. I trust the person who did my colors the last time. She really knew what she was doing, and she could explain why the other palettes didn't work for me but why people might have picked them. Every color in my palette works well for me. The best way for me to tell if a color is good is if it makes my eyes sparkle and change to a brighter prettier color especially if it picks up one of the teals, light blues or greys in my eyes. The other thing that happens is my skin looks brighter and clearer. I have rosacea, so I get a lot of pink and red, and my colors look great on me even without makeup. The red is minimized. However, they don't make me look washed out.
Enjoy your new palette. I hope you have found the pot of gold at the end of the color rainbow!