Exactly that's what I also showed a bit in the other thread. This is a quick and dirty sketch of what I've come up for now:

The lowest differential resistance of the tunnel diodes that I ordered is 14 ohms. So the effective load resistance of the load line has to be smaller. Right now the diodes are loaded by ~10+2 ohms plus the backwards resistance of the tunnel diode in series. I hope the backwards resistance is low enough otherwise I have to put parallel resistors to each diode.
This is IMO the most effective way to keep it stable. They can handle 0.6 volts and that's where the (high current) diodes and 1.5 ohms resistor come in. I used a lm386 to supply the generous amounts of current needed to power the diode stack. (Forgot to draw a a bipolar at the output of the lm386 btw, it will be there when I build it).
The 2 ohms resistor severely lowers the signal strength but it is needed to keep the load line more vertical than the tunnel diode characteristics.
I'm going to test all this first with a scope, doing some IV curves. I need to get this stable first before I start breadboarding it.