0. Most JT designs are crap. The most commonly seen scheme is a ferrite bead with some wire on it, feeding the base of a transistor through a 1k resistor. This is the worst way to do it, electrically speaking. Note that no one ever measures efficiency, they just make it light up an LED from a dead AA cell then throw it on the shelf to get dusty.
1. And speaking of efficiency, and metrics like that -- what do you hope to accomplish with a much lower startup voltage?
You can start from a heavily depleted alkaline cell, for example, but there's maybe 5% of full charge left in the poor thing. You're certainly not going to get much light out of it, by intensity or by duration. Better off throwing it out and putting in a fresh one (which will gladly start things at 1.5V, where you don't need to worry about Vbe).
Or if solar cells, why not use more, smaller cells? Same size, same area, different voltage and current.
Or if a TEG, you're barking up the wrong tree anyway, as you'll need quite high current capacity to do the job -- not something you'll find in BJTs.
Yes, germanium will do a fine job, but mind that most parts you'll find (if you do go looking for old-stock parts) are either small-signal transistors that can't handle hardly any current, or power transistors that are dreadfully slow (which doesn't rule them out for switching duty, but you'll need a much larger inductor). Ideally, you'd find a late model part with, say, 100mA Ic, 30V Vce, and fT > 20MHz.
2. Startup.
Si BJTs will keep running to fairly low voltages if designed for it, but won't start up.
JFETs can start in the 10s of mV range, but aren't worth a piss of power. Similarly with MOSFETs.
The most general method is to build a small startup circuit that kicks the main circuit into operation, using conventional logic and gate drives and beefy transistors however it does. This is obviously a little more complex than a transformer, transistor and LED.
Tim