> *The logic should be fully in hardware and no uC can be used. Any ideas
> on how to achieve that?*

It seems to me that you can draw-on the standard latching on/off control circuit used to power AC motors. They use a push-button to activate the motor via a relay and, a spare contact on the relay provides the latching function that your SBC (whatever that is). The stop button interrupts the latching contact and the motor turns off: -

[![enter image description here][1]][1]

Image from [here](https://electronics.stackexchange.com/questions/273676/latched-circuit-that-reverts-off-when-power-off).

So, if your two microcontrollers could activate another relay that replaced the stop contact, I think you'd be good to go. You could probably use an opto-device that replaced the stop switch also (saving cost and space).

  [1]: https://i.sstatic.net/R5TZL.png