Great info, I really appreciate your time putting this together!400' is ABOVE the maximum specified length for an ethernet run. The ethernet packet protocols have critical timing specs based on worse case progation times over 100 meters (330 feet) at the speed of signals in a twisted pair (about 40-70% of light speed depending on the wire). running longer WILL create problems, and this is even before we get into PoE voltage drops. In addition to the absolute propagtion speed, cat6 wire has 4 pairs, and each pair has a different twist rate, this is to reduce signal crosstalk, but it means the signals skew farther with longer runs, which causes yet more problems since both 100baseT and gigE use all 4 pairs, 2 for Tx, and 2 for Rx.
re voltage drop, AWG 24 (common cat6 solid copper) has 0.0842 ohms per meter at 68F. round trip on that 400 foot (122 meter) run will be 244 * 0.0842 = 20 ohms. 12 watts at 48 volts is 0.25 amps, 0.25 amps * 20 ohms is a 5 volt drop, so you would only see 43 volts at the far end. resistance goes up when the wire is hot, around 0.4% per degree above 68F (the spec temp), so the voltage drop will increase, too.
you can partially get around the PoE wire length issues by using a PoE switch or inserter that has a 'boost' mode where it outputs a higher voltage, however this won't solve the ethernet timing issues.