The reason PoE works on 48V is to compensate for the voltage losses across a long string of skinny wire.
The 'consuming' PoE device has circuitry to lower that voltage down to the 12V the cameras systems needs,
assuming it's working.
If the internal PoE board is bad and must be bypassed (which is unclear), AND you have a long run,
then you need to use a higher VOLTAGE of power supply into your passive injector/splitter (maybe 14-15v), not a higher current...
If you're putting in only 12V with passive injector, and you're running more than 20 ft or so, you'll have voltage drop
such that the cam won't be getting 12V. at 11V or lower, it might just not work at all. transient dips in voltage (due to
motors running or IR LED's firing up) will also cause the cam to reboot, like you are experiencing.
95% of these sorts of issues are due to faulty wiring. If you haven't bench-tested the cam with a short known-good wire
and known-good PoE or other power supply, you could fart around forever and never get it working right...