The thing you have to realize is that to use the 48V that you get from a "normal" POE system, the cameras incorporate a DC-DC converter to step the 48V down to whatever the camera really wants to run off of.  That might be 12V, since the camera has a 12V connection as well.  When you power the camera over the ethernet cable, the wire is quite small.  So using a higher voltage to carry the power through those thin conductors makes sense because you don't have anywhere near as much voltage drop in the wiring.  It's the same reason that long high-power transmission lines operate at very high voltages (so-called high "tension" wires).
If you want to run and back-up the camera from a 12VDC system, you can always just wire that 12V power into the camera's 12V power jack and not use POE at all.  POE is great for when you don't want to run a separate power cable and use a separate power supply for the camera.
But if you're going to end up kludging in some sort of non-standard power into the ethernet cabling, it will likely be a lot more trouble than it's worth.
As fenderman has said, just get a normal POE injector and then use a normal UPS to power the injector.
I understand what you're saying about how multi-conversion UPSs are inefficient, large, expensive, etc.  But they do serve a purpose.  You could power your PC or NVR as well as a POE switch (or power injector) all from the same UPS, and solve all of those problems at once.  To make the system work, more than just the camera will need to be battery-backed, if I understand your setup.
Building or buying a 48V DC UPS seems like more money and trouble than just buying a typical UPS that provides the usual mains power for your area (120VAC here in the US).