Hi Mike,
I can't give you scientific values for your question. But I guess, if you compare your subs without the moon and the subs taken with the full moon out, you will recognize the difference in contrast quite easily. I live in a bortle 4 area and I am not used to your bortle 7-8 sky. All I can say is, that you can still shoot good images with the moon out, as your example of M31 above prooves. But I can hear the screaming photographers shouting at me right now. Of course, it is not as much fun or effective as under dark skies or without the moon.
Shooting with your DSLR may not be the best option in heavy light conditions or with the moon out either. Using a CLS filter is a first step in the right direction. I had the same issues and decided to go for an astro camera and narrowband filters. They are not perfect for your kind of situation, but they work much better.
But the point is, that you may have to collect much more data than in dark and moonless nights. You also may decrease your exposure time and shoot more subs instead. As I already said, this is not as much fun. But personally, I bring the equipment out and still take images. Thats what I love and if I have to use the subs of multiple nights, I'd just do it. Image processing is a bit harder and the best images you will have, are maybe those of the nights with better conditions. I would suggest, you use the opportunities you have. Good conditions are quite rare

Don't know, if that helps you, but it is one opinion you might think about…
CS
Christian