Hi, RYNO - I did a bit more experimentation with this and finally determined that the switch port is the culprit. I did this by reversing the connections of the two IAPs on the switch. When I plugged the 'normal' IAP into the port that the problem IAP was connected to, the problem followed; likewise, the one that was acting wrong worked normally when connected to the other IAPs switch port.
From what I can determine, on the 5412R zl2 switch, there's an option at the port level to enable LLDP Detection. This was enabled on both the switch ports - but the one that was working correctly was able to use that setting so that the PoE 'Allocated By:' parameter set itself to LLDP, which is apparently necessary; on the broken port, the PoE 'Allocated By:' parameter was set to 'usage', and I was unable to change this, nor could I disable and then re-enable the LLDP Detection parameter - the command looked like it 'took', but the setting never changed. I eventually decided to try configuring a different port for the IAP, connected to it and that solved the problem.
Why this behavior never manifested itself before, I don't know, unless there was a problem with that port that simply didn't show up until PoE device re-booted - that's just a guess.
Both IAPs working normally now - hoping that this was just a single port issue and won't recur when I go to upgrade the other 200 or so IAPs in the school district.