By all means get one of GRJ's LED lighting boards to experiment with.
But I'll take your question at face value and answer it this way. It can be done using a so-called step-down/step-up voltage regulator module from eBay plus a few extra components. It would look something like this except with a much larger capacitor.
You can read the arcane technical details and get a feel for the level of soldering, wiring and component-level fiddling in this blog posting:
http://www.jcstudiosinc.com/Co...-Using-12V-LED-Strip
When all's said and done, the LED circuits reduce lighting power by a factor of 10x or so. So, in round numbers you need to store about 10x more energy than in the LED circuits. The energy storage is done in the capacitor so that's the key variable.
Whether LED or incandescent, you need energy storage and no one has come up with a practical way to store "AC" energy so you need a DC storage device (capacitor, supercapacitor, battery, etc.). In both cases the circuits convert AC to DC using a bridge rectifier. In both cases some regulator circuitry is used to deliver constant power from the storage device to the lights. In both cases you now drive the lights using DC - LEDs require it and incandescent bulbs can go either way.
So if you have the space to install the parts, I'd say less than $10 per car via eBay...$2.50 for the regulator module, a few bucks for the capacitor(s), and a few bucks for the assorted "glue" components. The circuit would have 2 input wires from the track voltage, and 2 output wires to the lights; in other words the same kind of modification/hookup to the LED lights.
Incandescent bulbs have a warmth that can't be duplicated by LEDs with present technology. Some, maybe most, guys will say they can't see the difference or the benefits of LEDs far outweigh the difference. To each his own.