You might try it without a voltage regulator. I have an old Simpson 260 that had the 15 volt battery that probably is no longer available.
I put two nine volt batteries in series( 18volts) and it worked out just fine. The variable rheostat that sets the peak needle reading compensated
for the increased voltage of the two nine volt batteries.
EDIT: Oops! I see you already tried that. I usually set my needle before use anyway.
If you want to reduce battery voltage put one or more forward conducting silicon diodes in series with one of the battery leads, each diode will drop about 0.7 Volts. Select diodes for suitable current rating.