I stopped at the mouse ........ and wondered why you would try to hack in a phone battery when you could use rechargable AA(or AAA) batteries.
Doesn't make any sense to me.
The POE idea ...
I see no need whatsoever in hacking the router. In fact I think it is completely undesirable. What if you want to change the router?
The ethernet cable is hacked at the source end to inject the power from the PSU ....... and if it was hacked again at the destination end to take the power out of it, then there would be no need to hack the router itself.
Because the PSU output cable has been cut, the 'left-over' piece with the DC connector is available and suitable.
Just does not make any sense.
Most of the others did not interest me ...... but the two that did I say were FAIL