...My concern was that at "idle" the 15.9VDC that the wall wart was producing would be too much, though at 1A draw the voltage would be 12VDC...
A quick solution for that would be to throw a big fat 15V zener
diode across the output. It will draw enough current at peak
voltage to keep it down to 15V, but won't draw any current
at full load.
You probably want to check the actual current draw with no
load on the supply to determine the power dissipation, but
a 25W device should be way more than needed.
Actually, a smaller zener diode used to turn on a 20A power
transistor may be a cheaper approach that could handle
higher power.
A bit cruder than a 3-terminal regulator, but enough to limit
the maximum voltage. Just depends on what parts you happen
to have in the junkbox.