Hi McGuinn,
Thanks for looking at my suggestion,
however,
you have muddled up a couple of little bits.
The extra efficiency i suggested is from using a type
of regulator that does not waste power.
Did you check out that page i gave ?
**broken link removed**
Most regulators do not act like that.
And you are correct that when rectifying and smoothing
the 6volt ac you get 9.1 volts.
However,
you can also rectify it and smooth it the other way
round, and get a negative 9.1 volts.
If you arrange that the two 9.1 volts are added,
then this uses exactly the same ac supply,
but gives almost double the voltage out.
The AC supply can do this without any change.
You can use the same AC supply to give 9.1v or @ 18v
simply by altering the rectifying arrangement.
Doing this will not require the AC supply to be
altered or changed in any way.
A higher voltage will hold more potential power and
in conjunction with a higher efficiency regulator
may give you the three seconds you need.
It may even give you some extra time using a standard
regulator unit.
Using larger capacitors will help with the supply at
9.1 volts, but the rate of voltage drop will soon
bring it down below the regulators range, by
increasing the voltage applied to the regulator you
will improve matters, if you also increase the caps
you might get it to give three seconds simply by
using the doubler as shown and bigger caps with the
regulator you are using now.
I hope my attempts at an explanation can be
understood, its not easy trying to explain the
actions of electronic circuitry.
Best of luck with it, John