So I did the check valve test with the chinese part and it was a no go. The check valve internal blocage piece couldn't handle the pressure and was stuck half open.
Here is what I got from this experiment so far:
Treg does start even if the left pump is disconnected, I mean electrically disconnected.
My left pump does not supply enough pressure so I couldn't start the engine with right pump disconnected.
When Treg starts with both pumps connected the left pump is shut down after a few seconds.
Left pump failure is mainly due to two thing: tear and wear of the pumping system (propeller and motor) and failure of the non return check valve. In my case the pump is almost dead in terms of fuel pressure but what is causing the treg to fail to run above 1/4 fuel fill is the left pump check valve. When the left pump is shut off by the system the non return valve is there to close the line and prevent fuel from flowing back through the pump and causing a leak in the 4 bar pressure required by the engine. The Check valve is so worn out that with more than 1/4 fuel fill the Treg simply refuses to move. When engine is started the pressure goes up to around 4 bar, there is even excess fuel dumped back to the fuel tank through the regulator, then as soon as the left pump is shut down pressure goes down to around 2 bar and the treg starts shaking when I drive it. It does drive slowly around 30/40 kmph and sometimes it stalls completely. When the fuel level goes back to the red zone and the refuel warning message appears the ecu activates the left pump and this helps act as a barrier against the fuel pressure coming from the new pump and the Treg drives pretty good even accelerates like a rocket with the 220 HP VR6

0 to 100 in less than 20 seconds
So here is my theory:
The left pump is shut off almost all the time, except when under load or when fuel level is less than 1/4 => More work and strain on the check valve.
The right pump is active all the time => less strain on the check valve.
This leaves us with the following conclusion:
The check valve of the left pump is closed and fighting against the pressure almost all the time.
The check valve of the right pump is in the open position almost all the time.
And this leaves me with three solutions:
Add a check valve (a good brand like the Pierburg one) on the left pump. I'm talking about adding this to my modded fuel lines and fuel fuel filter. It can be done on the OEM setup of course. You will need a submersible fuel filter and some ear clamps and quick disconnect connectors.
Put the right pump I removed in the housing of the left pump. This is supposing the right pump check valve is still strong enough.
Get a new pump. This I will do if my theory is rubbish and the two first solutions fail

A used pump will be dissected later to have a proper look at the internals.
Honestly I can't explain it otherwise. I can't find a leak in the system or the injectors. When both pumps are running the Treg is very happy. Not a single hesitation.