Hi Mike,
That sort of arrangement would be much more economical on batteries,
however any current through the LED also flows through the limiting
resistor, so to keep this fairly low, how about making the supply
voltage 4.5 volts, three cells, that means the limiting resistor
would be using less power than the LED rather than more with 9 volts.
Also if you cross couple between the collector of the second transistor
with a high value resistor back to the first transistor, then you get
a slight "schmitt" effect and the LED should switch on rather than
wind up gradually. This could save a little on batteries too as it
would only come on when needed.
Best of luck with it, John