This technique works.
As I mentioned in my comments, I think that it is best to try to reduce the introduction of loops to the twisted pair wires.
Here I am using a 1 Ohm and 1.2 Ohm resistor spliced into pins 1 and 2 of my PoE cable, which is a Cat 5 cable. I will use a constant current power source later on to accurately measure their actual resistances, but keep in mind these type of resistors are subject to variance under temperature change.
The voltage across the resistors combined with the resistance value will yield current measurements, which can be summed up and multiplied by the line voltage to determine total system power consumption.
I did notice that after setting this up the signaling rate has dropped from 1Gbit down to 100Mbit (probably a higher quality cable could maintain 1Gbit, but I wanted to sacrifice a crappy cable this time), but power is delivered to the device just fine and the network connection remains functional so signals are traveling through fine.
I will make a measurement of the overall PoE voltage later, but I don't need a super precise measurement of power, I can cross reference my results against the (very slow-refreshing but seemingly precise?) value reported from my Ubiquiti PoE switch.
In the specs of this switch it mentions that pins 1 and 2 are "power +" and this is consistent with the "Mode A" power delivery. As far as I understand it, since Gigabit is supported this means that all 4 twisted pairs are being used for signaling. Given that I'm getting current through both even when the signaling drops to 100Mbit, and it is in the right ballpark:
(63mV/1Ohm + 70mV/1.2Ohm)*48V = 5.8W
The switch reports 6.5W.