Adding the 1M resistor will make it to turn on immediately again when plugged in and upper sensor will turn it ON/OFF instantly when water level goes above and below. Looks like the lower sensor water level is registered as no water.
Will test it with the actual tank later.

 

Looks like finally home run!
Same problem using it in the actual tank when resistor is installed.
So 1uF cap only.
Noticed that the sensors were way more sensitive. (perhaps after the resistor fireworks?)
The bottom sensor detected my hand 1.5" away so I disconnected the sensor connector and pushed down the calibrating button for 10s or so. Reconnected, calibrated both sensors with full tank and to my surprise now working again!
Used the machine the whole afternoon, and not a single false trigger.

I hope this is it!
Will update in couple days again

Thank you !

 

Happy to report that 2 days of heavy use, and no single false trigger!

Now I have to see what happens if the machine is disconnected for while, if sensors keep their sensitivity calibration.
I hope they will

 

So, looks like I'm all done, everything working perfect.
After many days of use, also kept one machine disconnected couple days and sensors kept calibration!
So happy!

Thanks again! especially to @sghioto