TI has a more or less all-in-one solution in the TPS23753A. That chip is a 802.3at PoE device controller combined with a DC-DC flyback converter controller.
I've decided to go for gigabit Ethernet compatibility. That means insuring that the magnetics modules are gigabit compatible. It also means using a quad magnetics module with center taps. The center taps on the primaries are grouped into two pairs - the 12 and 36 center tap are one pair, and the 54 and 78 center tap are the other pair. Each pair feeds into a diode rectifier bridge, and the outputs of each are tied together to form the input into the chip.
This solution works even in the case of PoE injection just using the "spare" pairs as the voltage feed. In that case, no differential signal would come through the transformer, but the center taps would still carry the voltage. The rectifiers insure that any variance in polarity between the pairs is accounted for.
The controller will be configured for 5v out, and can supply up to 13 watts - plenty for a Raspberry Pi. It'll come out to the power pins of a USB A jack.