I have read that removing uterus will cut blood supply to ovaries, and impact ovarian function, even tubal ligation can damage ovaries.
As for LC and estrogen connection, there is one IMHO. Estradiol as well as other steroid hormones, made of Cholesterol, and it also takes saturated fat to make cholesterol, so diet higher in fat and cholesterol will result in higher estrogen. Carbs (especially whole grains and high fiber vegetables), block some of the estrogen from being re-absorbed from intestines back into liver, and carry it away with waste. So low carb can alter steroid hormones production in our body.
Fat cells make estrogen (estrone) mostly when ovaries shutting down, during and post-menopause. Before that estradiol is principal female estrogen and is made in ovaries. Being overweight messes up all hormones in general because of higher insulin level, that impairs ovarian and adrenal function in young females.