Report back again.
I took my fuel pump assembly to a shop and the guy tested it very well - he said he wanted to find a reason to find the pump bad and sell me a replacement, but couldn't, so I have to find the problem's source somewhere else. And he did that for free..
So I wanted to eliminate the O2 sensors too from the possible causes, so I checked them, as I have a #33 FI code which is the #1 oxy sensor, and even if I swapped with the other (which is working fine - I tested them, the #1 O2 has a problem with it's heating coil but #2 OK), and the code was still #33, checked the harness to the ECU connector and it was also fine.. So I cleaned the sensors , put them back but disconnected them, insulated the harness connectors with dielectric grease, rubber glove fingers & zip ties, took out the O2 heating fuse, and rode another 200 kms with my gen2. Worked well, but the stumbling problem appeared a few times again: giving a handful of throttle @ mid rpm-s (around 4000-6000) it was like switched off until I backed down the throttle. Thinking about it it is most likely the TPS sensor, and maybe it can make the ECU to completely shut off the fuel and / or ignition.. so I checked the repair manual just to find out, that unlike for my ex-R1 RN12 for which was a TPS sensor recall, @ kawasaki they thought that much better to have replace the complete throttle assy for around $2000 than just the sensor(s). Fook them... So my next task to check the TPS sensor & also check out if I can replace only the sensor. (on my ex Speed Triple, the service manual had instructions to replace and adjust the TPS, I dont think that kawi's have to have "factory precision" )
Other culprit for the shut-off (fuel sys) could be the kill-switch, but I checked it and it was fine, I cleaned it anyway and assembled.
The tip-over switch also can kill the engine (ign/fueling), but I don't think that could be the cause.
Fuel pressure regulator - but that was checked by the guy as soon as I gave him the pump assy.
ECU - if that is the cause I don't think that could be tested.
I liked Kawasaki before, as my older (ex) ones gave me many good memories, but I'm starting to be a bit disappointed in my choice. I hope I can sort it out and only the good times will roll instead of the bitter taste (of defects by design).