sama

sounds like progress. Next thing then is to figure out what FP control settings will make it behave properly. 
Try changing the polarity of aux2 to high and see if the problem get better/worse. 
can you hear the fuel pump at idle? Maybe have someone put their head in the boot and check? I'd be tempted to disconnect aux 2 from the ecu temporarily (cut the wire, un-pin it from a connector anywhere between ECU and FP controller), then at idle (so pump is running), connect it to ground, then floating, then 12v and see which connection makes the pumps jump up into high flow mode. From there you can work out what to configure in the ECU, or if you need to add a relay to deliver the right voltage.

In simple terms, the FP control system is set up so that the ECU tells a separate fuel pump controller whether to run the pumps fast or slow. It does this by sending a voltage (or ground) signal down the aux2 pin when certain cirteria are met.
Relevant parameters to your situation are:
RPM threshold: the RPM at which point the signal is sent down this wire to the FP controller
DC%: injector duty percentage - works as an OR operation with RPM. If you go over this injector duty cycle or this RPM then the control voltage is sent to the controller
polarity: whether the "switch to high mode" signal is to send ground or to send "nothing" (ie the "go slower" command is to send ground).
The expected state of the FP controller are:
off (when the fuel relay is turned off - not relevant here)
slow: some pwm'd low output mode
fast full flow rate.
 
What i've been trying to explain is that you need to identify how the voltages on that FP controller input (aux 2 output) affect what the controller does with the pump speeds. It sounds like the "dont do anything" signal from the ECU as it stands is "fast mode". This will work fine if you just set both thresholds to really high numbers (10k rpm & 99%DC), but this means you dont have a "slow mode" option for low load times. It just means your pump is noisy-er and wears quicker. If you want to reconfigure this to the point where idle-ish loads swap to low flow mode, you would first need to identify what the signal is that makes it swap to high flow mode, then configure the ECU output to provide that signal. Note that some outputs can send 12v or ground, and some can only send ground or nothing.
 

Your error low value for the Lambda is set to 1 Volt.  This should normally be 0.05 V or sometimes might need to be 0 Volts to suppress errors on start up.

 
Also, try the Link NTC1-8 & IAT1-8 Calibration and see if they are closer (that normally fixes the bottom end of the cal.)

There is no cuts or limiting out of the ECU so can rule out any limits. As CJ pointed out that ignition timing is odd and should be corrected. 
Fuel flow has been checked? Pump is running?

I think its something to do with your fuel pump control causing the pump to shut off or go into low output mode. The bit where your foot is flat, but your RPM is dropping is the key point for me. 
Can you get your wideband running so we can see if its going rich/lean while the revs drop at full throttle? Alternately, get a fuel pressure gauge/sensor installed?
Maybe try setting the fuel control cutover to something like 4k & 50% DC as a test, and if that makes no difference, try disconnecting pin aux2 from the ECU and applying straight 12v to it (which should force the pump to high throughput mode)

Your fuel pump set up and the fuel pressure increase solenoid on ign 8 all looks to be ok to me. 
Have you actually tried adjusting the fuel?  You say "stock engine" but the master fuel is set to 8ms.  8ms would be typical for injectors around 1000cc.  If you have the stock 440 or 550cc injectors then the master will likely need to be more like 13-20ms.
 
That doesnt sound like anything to worry about to me.  If you want to do a more scientific test, pull both sensors out and hang them in a cup of ice water.  

lambda going lean would line up with fuel delivery problems.
Because you have it working with a factory ECU we can likely rule out mechanical issues - blocked air or fuel filter, faulty fuel pump, bad regulator, etc. Based on this, this only this I can see in the config that would impact fuel pressure is if the fuel pump isnt being controlled properly by the link ECU. I'm assuming all the pinouts etc are correct, which just leaves the fuel pump control being wrong - maybe its not sending the right signal to run the pump at full power, maybe the PWM signal needs to go to 12v instead of ground or vice versa. Looking at the wiring diagram, these dont run a simple on/off relay, but a separate fuel pump controller, and there is a pin that is PWM'd to tell the fuel pump controller how hard to drive the pump.
My money is on the config for this pwm signal being wrong (or maybe on the wrong pin, so it stays on low power at all times) - hence my suggestion that if you dont see any improvement from ecu config changes, put ground or 12v straight to the controller so it runs full power, then you know what the voltage needs to be and can work backwards from there to make it happen.

An volt 11 & 12 on the expansion connector is correct as per the top photo.  The second picture you show of the "pin functions" list is for the 2007 ECU, not the 04-06.
So AN Volt 11 will work provided your wiring and cal table is correct.  You can attach your map if you want us to confirm the cal table is set up correctly.

If you couldn't find the sensor data you weren't looking very hard.
https://aemelectronics.com/files/instructions/30-2010 Sensor Data.pdf

It looks like it is the same sensor we sell so you can use one of the built-in calibrations.  Set up like below.

Hi Sama,
The BAP is enabled from the factory, if you open the Runtime Values Window (F12 key) and look at the 'General' tab you will be able to see the current BAP reading in the left hand column. Here is some info on the accuracy at various temperatures:

Scott

works perfectly, almost matches AIM GPS wheel speed misses by 2 km/h, now ready to play with traction control