What have I missed?
Do you have twin tanks (i.e. ex-military 109)?
If so, check the cork seal in the changeover tap. I've had issues going back some time with the ambulance, it's had 3 fuel pumps and 2 carbs and still exhibited fuel starvation (worst under load) and I only discovered last week the fuel tap was the culprit, swapped that for another and it's as good as gold now. Cork seals can be had on eBay for less than 3 quid.

Other than that, Jim speaketh the truth. The Weber 34ICH is fit for target practice but not a lot else in my experience, a Zenith or Solex is the way to go.