First Step Examine the carb

have a look on Hitchcocks motorcycles I get most of carb part of them  Monobloc Concentric
and they do tuning tip sheet on how to set it up you can down load it

number is on the top of the flange

main jet  250

pilot jet 25

throttle valve No 3

needle groove 3

Carb looks like std fitment , monoblock 376 . A sonic bath is good but does not usually clear the very small pilot drillings fully . The slide and body are likely to be both worn enough to make slow running and clean pick up elusive but will work enough to use. 

well put Robert. Just it running then deal with fault and worn part oil leaks 

Looks more like inch and a sixteenth than inch and an eighth.  376 on the flange will confirm it's no bigger than that.

Hope I'm not being too obvious, but that air slide has to be held up out of the air flow for normal running.

Info I have on the 376/50 carb is - 
Norton 596cc 1955: 19R Twin (Export)
Bore . . . 1 1/16"
Pilot . . . 25
Cutaway . . . 3
Main . . . 250
Needle jet . . . 0.106
Needle position . . . 3

Which is same as Tony's above, Hope this helps

number 31 is a jet block it has gasket on the base and is a tight fit, ME myself would sonic clean the lot. no emery tape . polish the slide and bore with solvol autosol . and try it on the bike. it easy to add new bit . you may fit new now to find the body is worn out.. the most you need is a gasket 
washer kit PS you can use a very fine  wet and dry paper    

You have certainly made a difference to the parts. The throttle slide should fall down by its own weight, with no help from the spring or cable attached. Under the circumstances (all nice and clean) I would think any resistance would be distortion somewhere. I wouldn't apply any oil, it will either be washed off or gather dust if not.

Any distortion jamming the slide will likely be in the carb body not the slide itself, usually from overtightening the flange nuts. Have you tried the flange on a dead flat surface to see whether it is bowed at all? Sometimes they can be carefully persuaded back into shape as simply fileing the flange flat again won't take out the distortion in the carb body bore. Your slide does look a bit scored though.
Best regards, Al.

When the flange bows it pulls the body out of round and slides stop sliding, Better to press it all back to the orriginal shape. I have however persuaded oval bodies back into use with gentle sqeezing with an adjustable grip while checking with a vernier caliper . I also think the problem can be caused by years of heat cycles and missing/poor  insulating spacers.removing metal is usually fatal to slides .Slides can also go out of round and benefit from a squeeze.

You say:-

The part the throttle valve sits over (Could not find the name on the Amal drawing number 31) was jammed in tight and took a few light taps to pop out. 

It should be jammed in tight. Normally gentle application of heat to the body would be required to remove it, and the same to re-fit.

I lubricate the slide with a thin  smear of molibdimen sulphide grease, (universal joint grease) . 

just downstream of the spray tube.  Depending on the amount of throttle opening it may pass air or fuel - but being very tiny indeed it is prone to blockage with dried fuel.  The most obvious symptom is a slight stumble as you begin to open the throttle from idle as you pull away.  To clear it I use one short strand from a bicycle control cable, a pair of tweezers and a magnifying glass so I can see that I am doing. Just gently poke it in that little hole.

I know the books say a 376 for the 19S, but in my opinion a 600 single would be better with a 389 - 1-1/8".

is very tiny, and I suspect that a sonic bath may fail to clear it if blocked. 

Just stay with  what you are doing. mate . and get to the IOM    Ps i have booked for the MGP

The slides tend to wear more than the body.  The monobloc you have has the slide better supported than the later Concentric type so yours is not as prone to wear as a Concentric.  Even so, I would buy a new chrome plated or hard anodised slide.  They last much longer.  It's not good engineering practice to used the same metals in two parts rubbing together unless they are self lubricating like cast iron.