I've mostly been doing component research and gathering user input for now, instead of jumping in and starting detailed design.  I've definitely learned a lot doing that and a direction is starting to take shape.  Here are some of the things I've learned and conclusions I've drawn:

• There is "proper" standard 802.3af / 802.3at PoE and there is so called "passive" 24V non-standard PoE.  Proper standard PoE uses a nominal 48V voltage, accepting 37V-57V.  While it would be nice to support everything, including passive 24V PoE, supporting such a wide input voltage range would definitely complicate things.
  Consider just the input power.  To support the 802.3af PoE Class 3 (12.95W), at the minimum input voltage of 37V, the components need to deal with a current of 0.35A.  When trying to support passive 24V PoE as well, components need to deal with 0.54A to allow the same output power.  More actually to account for higher cable losses.  At the same time everything needs to be rated for 100V as well to ensure reliability, driving up component cost.
  Also, the flyback transformers used have a certain winding ratios that works to produce close to the desired output voltages based on expected PoE input voltages, in the duty cycle ranges PoE PWM controllers are designed for.  Having to support a wide input range from 24V to 57V again complicates things in having to ensure the PWM controller works reliably and is stable across a wide range of PWM duty cycles.
  Moreover, many PoE PD controllers have undervoltage protection that needs to be bypassed to even work at 24V (if possible at all).  There are also very good reasons the 802.3af standards people chose such a high 48V voltage: to keep currents low and reduce losses over long, thin gauge Cat 5 cable runs.
  All in all, "passive" 24V PoE seems to be just an ugly hack.  Yes, you can cheapen things just a bit more when only doing passive, but when trying to support both it definitely complicates things.  Yes, you can get passive injectors cheaply on Amazon for $8, but you can also get proper 802.3af injectors for $12.  For that small a difference, I really don't see it as a burden to the user to only support standard 802.3af PoE, which is what I intend to do.
• If a PoE design has no touchable metal parts or is not connected to anything locally powered, it is acceptable to make the power supply non-isolated.  This would make the power supply a little simpler, more compact and lower cost.  However, since I can't guess how anyone might use a base board like this, and I intend to have a local programming port that can be connected to a computer, it seems unwise to do this.  So I have decided to avoid any issues and make the power supply fully isolated.
• I had expected to be able to save cost by doing a low power (3W or 7W, Class 1 or 2) instead of a "medium power" (Class 3) design, but it turns out to not make much of a difference in cost.  It looks like one flyback transformer capable of supporting Class 3 just fine (PA2467NL) is actually the lowest cost option at various distributors.  In the volumes I'm looking for (hundreds), it's cheaper than even the 3W flybacks.  Must be a matter of volume.
  Various people have suggested I do 2 versions: a low cost low power one, and a higher power full featured one.  But it looks like power may not turn out to make much difference in cost.  It would make a difference in size though, so I may in the future entertain a low power version for that reason.  For now, I'll focus on a more generically useful "medium power" version.
  I say "medium power" because with the 802.3at and 802.3bt standards it is possible to get much higher power out of PoE.  But if working on the #LiFePO4wered/Pi+ has taught me anything, it is that supporting high output power is not trivial and you run into all kinds of unexpected issues.  For now "medium power" Class 3 12.95W power seems like a nice target.  For most users this will be much more than they ever need, but since it's not going to add cost it seems to be the way to go.  And in addition to sensor applications, it will allow "actuator" applications as well (LED lights, motors, solenoids, speakers, ...)--the applications typically causing issues with wireless and requiring wired power.
• At first I was bummed to find that the low cost PA2467NL flyback mentioned above is a model designed for 12V output.  Since the ESP32 requires 3.3V, I had been looking at making a single voltage design to reduce cost, by removing the need for another regulator.  However, as I thought more about the use cases, I became convinced that having both 12V and 3.3V available was actually an excellent option.
  If you consider what you can do with 12.95W of power, it is very unlikely you want to use it at 3.3V.  Consuming 12.95W at 3.3V would take 3.92A current, requiring fat PCB traces, 2oz copper, and leading to high losses and heat production.  Consuming the same power at 12V requires only 1.08A.  That's why it's so common to find 12V LED strips, motors, solenoids, sound subsystems etc.  Having both 12V and 3.3V available is perfect as far as I'm concerned.
• While working on the custom PoE design I just finished, I had found that most common Ethernet jacks don't support PoE because they don't provide access to the data pair's center taps or the extra UTP pairs.  You need special jacks that are made to support PoE, so I ended up using a fairly expensive jack in that design.
  Now in my search for a low cost alternative, I came across some interesting Chinese options that not only integrate magnetics and high voltage termination / protection caps and resistors, but also the diode bridges required for PoE, all integrated in nice compact jacks.  This will save a good amount of space on the PCB.  The jack I'm likely going to use is the HanRun HR861153C.
• In my search for a PoE PD/PWM chip, the Silicon Labs Si340x family jumped out due to their low cost and high integration (bridge rectifiers, TVS diode, power MOSFET).  At first I was focusing on the Si3402-B because of the integrated diode bridges, but when I found a source for the Ethernet jack with diode bridges built-in I shifted my attention to the Si3404-A because it is lower cost, still has the required TVS and supports higher efficiency in the power system by using the auxiliary winding on the flyback transformer.
• I was intending to use the low-cost CH340G USB UART bridge for the ESP32 programming interface, since it's cheap and has worked well for me.  But it was brought to my attention that this chip has suffered from continuous driver issues on Apple Macs.  So I might change over to a Silicon Labs CP2102N instead.  It is significantly more expensive than the CH340G, but it also results in a more compact solution saving PCB space, and it seems wise from a customer support standpoint to not design in a part that causes support headaches.  I trust no one has seen driver issues with the CP2102N chip?