This phase II trial studies how well Avatar-directed chemotherapy works in treating patients with ovarian, primary peritoneal, or fallopian tube cancer that does not respond to platinum anti-cancer drugs. Drugs used in chemotherapy, such as paclitaxel, gemcitabine hydrochloride, pegylated liposomal doxorubicin hydrochloride, topotecan hydrochloride, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Monoclonal antibodies, such as bevacizumab, may interfere with the ability of tumor cells to grow and spread. Using an Avatar, a living tumor sample with similar genetic characteristics to the original tumor, may help determine which chemotherapy is most effective.