Some prototyping and it's done !
There is something strange with the CMOS inverter: the circuit does not work when a BS250 replaces the 100K pull-up. The mystery is still complete.
Another hickup is the pull-up in parallel with the LED: without it, the LED drop does not allow the next gate to rise high enough to propagate the wave. That's why the original circuit worked at 6V...
I try to make it as efficient as possible so I'll increase the resistances even more.
There is no series resistance with the LED because it's a 1W model (can easily stand 200mA), it normally works at about 3.2-3.5V and the scope shows the maximum drop is 0,3V, so the peak LED voltage is around 2.7V is short bursts. No heat is generated.
Power consumption without the LED is about 50µA, I replaced the 100K pull-ups with 330K and it drops to 18µA peak (10µA in average ? I can't measure slow currents in RMS). This is very low, the LED consumes much more current, and the higher resistances slow down the transitions...
Now, WHY does the circuit stall when the BS250 replaces the pull-up resistor ?