Phew, that was a journey. This project really started killing me slowly... It worked at first but the damn thing tried to die randomly. As I put a 5V6 zener directly into the 5V rail (the reg. has a short circuit current of 20mA only so the zener does not need an resistor) at least the Attiny861 follow the regulator each time it blew...
I tried everything and always thought: Ah, this works now. UNTIL it blew again. Mostly on (re)connecting the LiPo battery. So it had something to do with the inrush current.
When I talked with @Simon Merrett about the issue, he suggested to limit the inrush current to the regulator with a resistor. First I though this is a bad idea because additional resistance in the path means more (quiescent) current.
But I gave it a go. In the above picture you see a 10 ohm botch-resistor. It effectively kills the inrush-current to something which doesn't destroy the regulator.
NOW IT FINALLY WORKS like... ALL THE TIME. Nice!
Just tested the board with a 6S LiPo and a electronic load. You can switch a constant 175-180W without the MOSFET getting more than luke warm.
Off-current is 13µA. A bit much for my taste (should be more like 5...8µA) but I guess it's got something to do with the reverse leakage from the 5.6V protection zener (though the datasheet says 2µA reverse current max...).
I'll do some more tests soon.