After being diagnosed with stage IB cervical cancer in October 2012, Allison Pozzi consulted four different specialists near her San Francisco Bay home. Every one of them said she needed a hysterectomy, which would’ve prevented the 35-year-old from ever becoming pregnant.

“My husband and I were newlyweds — and I’d had a miscarriage shortly before my diagnosis — so it was incredibly hard to think that this experience was being taken...