Answering myself in case anyone else runs across this...
The burned component is a Littelfuse SMBJ15A transient voltage suppressor diode.
The center pin of the power connector goes through one winding of the transformer to the anode of CR6, a 4A, 40V Schottky diode.
The shell of the power connector goes through the other transformer winding to the anode of VR2, the 15V unidirectional TVS diode.
Circuit common is at the anode of VR2 and the cathodes of both diodes are connected together.
The input appears to be 15V DC, polarity, over-voltage, and transient protected. His 15V power supply outputs an unregulated 20V.
After removing the TVS diode, I inserted a current-limited DC voltage at the cathodes of the two diodes and the unit works. It's charging now from my bench supply. It looks as though I got lucky.