Don't be fixed on the idea it must be fuel because the choke has an effect. A faster flywheel and less inlet vacuum to pull against will help overcome any loss of engine power. A richer mixture can also help ignition from a poor spark or compensate for an air leak downstream of the jet.
If it was a fuel supply issue, the choke would only have a short lived effect as the float chamber empties faster.
Have a look at the spark plug colour immediately after it starts playing up and give the ignition the once over. You don't need the engine to be running, like you do to set up the fuelling and without correct ignition performance you'll never manage to test & adjust the fuelling properly.