5.4:1
Does this mean that you have a gear box on each reducing the drive by a ratio of 5.4 to 1? If so, then much of my concern here is reduced. This motor is simply not designed to turn a large prop directly. A small ducted fan yes. 2.5" ducted fan. Your large prop, even with the low pitch, would cook things if they were put on the motors in a direct drive configuration.
Parallel 11.1 - Good, that keeps the voltage in the range that the motor (and presumably the controller) expects.
I purchased a watt meter for my motor tests. This is very useful in tweaking a power system. It tells me how much current a motor is pulling with a particular prop. If the current is too high, then you need to go with a smaller prop. Too low and you can try a bigger prop. But without technical information on your ESCs, this would be all guesswork. If you know that your ESC can safely handle 10 amps, then you can measure and make sure that it stays under 10 amps at full throttle.
When you get pictures, I am interested in the burn components. But I am also interested in detailed shots of the undamaged ESCs to see if I can identify them.
Don't worry about your use of the English language. It is better than many who were born into it! But I think the word you are looking for is 'thrust'. The smaller propellers are likely thin. They flex under excessive load and lose their thrust.
Also, a propeller attached facing the wrong direction also produces very little thrust, so you might want to double check.
If you have access to RC servos, it would still be valuable to hook them up rather than the ESCs. This would confirm that all 4 output signals are working properly.
Is your aircraft going to be autonomous or radio controlled? If RC, then you can hook the ESC directly to the receiver to test the ESC and motor with the RC receiver and transmitter.
It is certainly still possible that you have a bad controller. But I would want to perform tests on distinct units.
I do not know that your board is sending out 4 proper servo signals.
Connecting RC servos would perform this test. If all 4 servos move properly in response to your board sending various throttle commands, then we would know your board is behaving properly.
I do not know that all 4 motors and the 3 remaining ESCs behave properly.
Connecting the ESCs and motors to a receiver to confirm that they respond properly at all throttle levels would let us know they are behaving properly.
As a side note, I also have 4 motors 4 ESCs and props for this kind of experiment. 4 inputs from the RC receiver, some inputs from gyros and a little bit of software and I should be good to go!
It is really that 'little bit of software' that I am looking forward to.