Read the manual, it turns out there are 3 models of this AP, -DC, -AC, and -P. Only the -P version can
run from PoE, the -AC and -DC versions need dedicated power and can
supply PoE. As you might expect from the AC PSU, mine is the -AC model, so no love for PoE in.
Did a little hackery to see if I could get the PSU working before I ordered parts to fix it proper, figuring if the PSU is still viable the rest probably is too.
(Yep, it's a scary sight. Make like Alanis Morissette and keep one hand in your pocket! O0)
Jumped the fuse, bodged in the closest (in terms of voltage, at least) cap I had on hand, and after putting on my face shield, plugged it in.
~54V out just like on the sticker!
After checking the PSU output for ripple and other funk with the scope, I temporarily reassembled it. Looks like it's still alive, at least to some extent!
Status LED comes on solid green for about 10 sec, then switches to alternating red/green, which according to the manual indicates "booting, not ready". I don't know a whole lot about the operation of these devices, so at the moment I'm not sure if this is indicating a dead AP board, or just the AP board indicating it doesn't have a config or can't find a management/tftp/whatever server.
Another positive indicator is that when I plug an eth cable in the link light comes on and flickers with activity, so it appears some eth phy somewhere is at least partially intact.
I apologize in advance for referencing Alanis Morissette.