I learned the identities of some of the doctors who were on the scene first. Most health centers have some satellite phone access, and their doctors are permitted to move around the region. When I contacted two of them, they made it clear that they were afraid to speak to me after receiving threats from the army.
Later, we learned from @humanrightswatch of an army campaign to silence and intimidate doctors, many of whom provided info on casualties to journalists.
https://www.hrw.org/report/2024/07/03/if-soldier-dies-its-you/attacks-medical-care-ethiopias-amhara-conflict
Nevertheless, a doctor did confirm to me the hospital that they, the first only first responders to assist the victims, was located. They were staff of the Gawuna Hospital. This narrowed the search down considerably.
The village of Gawuna isn't identifiable on most maps, the hospital for some reason, is. Here is where the hospital is located, in rural Amhara country. It serves all of the nearby villages.
https://maps.app.goo.gl/28Tm33bhbWs7YXJS8