You should get at least one second opinion at a major hospital of high regard like Brigham and Women's!
HI!
There is definitely a reduction in the recurrence rate of breast cancer when the ovaries are removed. This has been shown in several fairly good, well done studies. A couple of other things to consider--the complex cyst needs to be removed anyway if it is persistent. If it goes away, I might consider watching and waiting.
Some other important information to consider is that Tamoxifen increases the risk of uterine polyps and endometrial cancer 8 times the baseline rate. You already have polyps, and probably don't want to risk another cancer.
You could theoretically leave the left ovary, and derive some benefit from it after the Tamoxifen therapy is over (usually 5 years). But if you were my patient, I think I would want to talk you out of AT LEAST the cystic ovary( if persistent) and the uterus.
By the way, if the cyst is benign, you could be a candidate for a supracervical laparoscopic hysterectomy, or a laparoscopic assisted vaginal hysterectomy with removal of ovary(s).
I'm sure that you don't want more surgery, but you even more don't want more cancer!
Good luck!
Dr B