Here's a chintzy way to adapt the 12V soft start circuit (v1.1) for 6V use.

There are more elegant ways to do this, but I was able to quickly hack the circuit to function in a 6V system, with a few parts I had on hand: I added an AA cell in series between R1 and the positive supply, and changed R1 to 4.7k. The battery raises the voltage "seen" by R1/D1 enough to keep the circuit pretty stable down to 4.5V or so on the main battery. The circuit draws very little current from the booster battery, less than 1mA in my test, so that battery will last a long, long time. With an AA or an AAA alkaline, it could last for years, depending on usage.

More elegant solutions would include, changing D1 to 4 or so volts, lowering R1 to keep it stable, and then adjusting R1/R3/C1 to set the appropriate turn-on timing. I don't happen to have an appropriate diode sitting around, though. (The big concern would be that Q1 might not stay all of the way "on" as the battery voltage drops, since its threshold voltage is so close to the supply voltage.) Another way would be to use a voltage doubler, though I haven't thought that through.

Seeing spots,

JAB