Missing at half to full throttle

Sounds like fuel starvation.  I had to drill out the fuel tap on the Rudge as it was so restricted by tank liner . 

The standard throttle valve cutaway for my ES2 is a 4. I found I had similar symptoms to yours before I changed it to a 3.5 and it transformed the running.

It's worth checking what Robert says as well - disconnect the fuel line and see how much petrol will run through in a specified time using a measuring jug. If we assume 40 mpg at say 60 mph you would need to see 1.5 gallons in an hour or 100cc or so in a minute. (if my back of an envelope calculations are correct!)

I recently renewed my needle jet and now the bike runs weak and hot, so even small things can have a surprising effect. The fact that your bike wont run on full throttle (when  the main is doing most of the work) tends to point to a poor fuel supply. There can be plenty of culprits.

The trouble is Fuel Starvation does not fit with the fact that the motor revs OK on half choke.

But I haven’t got any idea of what the problem might be. I’ll get me coat.

by using the choke you are makeing it richer by reducing the air intake

at that throttle opening its going to be a problem with the main jet have you tried raising the needle

and check jet size

These issues can be frustrating to solve even for old hands. You have to follow the clues but keep an open mind and expect it to take longer than you think.But how satisfying once solved.Just checked my needle position ,found to be one notch too weak . Was lowered years ago to correct rich running with the old worn jet.,now unhappy with the new jet. An easy fix .Now why has my throttle gone stiff?,  cable squashed when I refitted the tank!!. NEXT!.