The thing that gets me is you are figuring on the max the motor is capable of putting out. This does not mean you are going to be at 350 watts when you fly.
My thing is looking at the amps vs voltage and power.
Power = amps x voltage,
Or Power over Voltage X Amps
You have the voltage and you have the power 350 watts(motor Rating) so figure the current by dividing 350watts by the voltage used, 3 or 4s.
That will give you the max amp draw the system would be at given the voltage used, letting you know the size ecs that could be used.
Not what real time amp draw will be in flight.
That given 350 watts divided by 14.8 (4s) will give you 23.6 amps... per motor
350/12.6 (3s) = 27.7 amps per motor
These are max ratings So 30amp esc should be good on 3s or 4s with no problem
If you want more headroom on the esc that is up to you to get a higher rated esc. I use 30 amp on my Hexa with 10x5 props 3s setup. And 9x5 or 10x3.8 if I do 4s.
But in real time flight the amp draw should be no where near the max the system is capable of handling.
As far as the battery if you go 4s with 6 motors 23.6amps per motor will be a max 142amps
3s will be 166.2 amps
So your 3s 5000 30c should put out 150amps cont. as you stated and in real time flight should be fine for the 6 motors.
I fly my Hexa on a 3s 4000mAh 60c but it never gets warm, but I know it is a higher rating. But I have also flown it on a 3000mAh 30c too when testing my gains.
I would bet you are not pulling over 15 amps per motor in normal flight. But this is where an amp/watt meter comes in very handy.
The wires getting warn makes me think of the battery connectors as Tony said.
If you have a bad solder joint or a loose connector your wire will get hot by adding more resistance to the circuit.
It is like have a garden hose with a good flow and then squeezing it and the flow slows.
Current is the same way if you have any point in the circuit that is not making good connection it will increasing amp draw producing more heat.
As in the case of using a real Deans connector vs a copy cat look a like. I tend to use the connectors that are more like bullet connectors.
I use an XT60 on my Hexa with no problem.
Hope this helps, and not just confuse things..
