An additional idea...If you measure DC coming out of the wallwart
instead of AC, it likely just needs filtering. Skip the rectifier and
go with just the capacitor and the regulator. Maybe you could start
with a higher voltage wall wart, too. The 317 regulator can handle up
to 37 volts input. If you do that the variable voltage property of the
LM317 chip would be great to use for other items requiring a wall wart,
but one of different voltage. Maybe a 14 volt or 15 volt wart would be
a start. If it puts out AC, include the rectifier diodes. If not, skip
'em.