Examine ratings of existing headlight bulb ... calculate (bulb Wattage) / 6V = (battery Amps) ... I'd think it's given that modern high LED assemblies will always not-less-bright (likely far brighter) than old bulbs when consuming the same power, so basically just concentrate on finding something that physically fits nicely within the original headlight fixture and doesn't yet doesn't exceed the rated Wattage or Amps.
Resistor/capacitor/regulator components will take up a little space, and may require an externally-exposed heatsink, but probably not much. Possibly integrated within the unit itself.
I'm used to working with 5V LEDs ... I have no idea whether 6V and 12V versions are available for automotive use.
Can't you just purchase a screw-in LED version of this particular incandescent bulb? Or possibly mod a standalone LED version into the screw-in receptacle of a dead bulb? Perhaps a better option if you intend to keep the original collectible value intact.