Well i think we now know its a fuel issue!, one small saving grace.
I had a similar issue on an 8v golf, which i actually didnt fix when i sold it! However, I had done pretty much everything including electrics as you have done, plus ultrasonic injector clean, new fuel filter, fuel system cleaner, throttle body.
On this car it would sometimes cut out round corners when 1/4 or below on fuel, and had difficulty starting, from what i know of what i had done on that car, I would be thinking towards the fuel pump itself.
If you know its the fuel pump, I suggest a new one. However in the meantime it might be worth asking on here if anyone has a second hand one at a reasonable price which they know works just to try it?
Also, the things you have replaced, have you kept the old ones?, if so you could change them back and sell the new stuff you have bought to
help with the cost!
And dont panic, very little left to check!
p.s once you get it right with all the work you have done the car will drive mint believe me, and it will all be worth it! Ebay have some fuel pumps for about £30 ish. Dont know how good they are, but if you can do it for around that price i think its a good one to do. Ive never bought a fuel pump but im sure some guys on here will be able to
help. Also, try and get one already in the plastic casing around the metal pump, i wouldnt want to try to fit it otherwise, looks fiddly and easy to break!
However, petrol is nasty stuff, its no more than 30 mins to change the pump, however if you arent completely sure get a garage to do it.