1.8 carb dying uphill.. Seems an impossible fix.

I must've looked through every thread on this problem, and am yet to find the solution.
This problem is beginning to drive me insane, as selling the car is not an option, and I feel like the issue will never go away. cf_emoticons__BangHead:My MK1 has been breaking down when traveling uphill regularly for the past year.
Before this started happening, I had a similar problem on level roads, so replaced the tank and filler neck, which has sorted that, but it still breaks down 60% of the time going up hills.
Over the year, I've rebuilt the carb and fitted a new rubber mount, replaced the majority of the fuel lines, changed the filter, fitted new vacuum lines, fitted a new fuel/air separator which was then replaced with a brass t-piece, and a lot more, but my memory doesn't serve me well.
I also recently had the dizzy rebuilt and carb mixture done on a rolling road, after which, there is basically no fuel in the filter when it's running. It's not empty, but seriously low, I'd say about 1/8th full.

The car begins to splutter, then if I plant the accelerator into the floor, there is no power, only what feels like intense engine braking. If I drop a gear and hit the accelerator, the revs increase initially obviously, but still continue to fall until the car is no longer running. After about 10 minutes, the engine will usually start again and run fine.
It will run forever in idle with no problem, I've even been towed up steep hills while idling and the problem is not there.

The engine is the original 1.8 EX with a Weber 32/34 DMTL carb.

Any help is greatly appreciated.
 

Also, I had thought that it was the swirl pot that was the issue, as the tank is a pattern part, so probably has a low quality swirl pot, but the problem happens even when the tank is full to the brim.

EDIT: Got some decent weather, so just went for the first proper attempt at driving since the mixture was adjusted, and it is now happening under load, at around 3.5k revs.
Could it be the fuel pump?

sounds liek carb icing, though it is a bit warm right now? if its quite damp out this makes it more likely to happen. anyway check warm air flap opens with engien runnign and the pipe from the airbox to shroud on exhaust is there as well as the shroud.

should be a heater on the front of the carb which gets ignition live so look at that, and make sure the earth wire from carb to rocker cover is there

apart from that, you could try feeding the fuel pump outlet straight to carb and block off the return. if that helps you could try restricting the fuel return from the swirl pot, there was a thread on this recently