There are a number of companies (e.g. Mikrotik, Ubiquiti, Netonix, Tycon Power, PoE Texas) which produce a variety of so-called passive PoE products - mostly for outdoor APs and fixed-wireless access networks operating at nominal 24v (most common), 48v or 54v, but I've not seen much for nominal 12v.
Even though it isn't built in to the ONT you could potentially use passive PoE injectors to combine the DC + data over a single network cable if providing mains close to the ONT is problematic. Being 12v does limit the distance, you would drop around 0.5v on a 10m Cat5e cable for a HG8110 ONT which is fine. For longer runs you could use an active 802.3af splitter at the ONT e.g. https://shop.poetexas.com/products/gaf-12v12w
fed from a regular PoE switch or midspan injector.