I think all chokes of this kind work on the following parameters:
When the choke is pushed in it really must be fully Off at the carburetor end, not slightly engaged dependent on the springiness of the cable.
In the choke-in position the throttles must close so that their stops are just clear of the choke cams.
When the choke is pulled out it should should after perhaps 1/8 inch of movement start to engage the cams on the throttle stops so that the throttle opens to give a tiny amount of air, progressively more with more choke. ie not too choked.
I don't know what that equates to in terms of gap at the cam, but whatever it is is just a way of saying "open the throttle a bit as you pull the choke, but not before".
Every single carburetor car I have owned (Roadster, Mayflower, LandRovers, Stag, Volvo 240s, Renault 4, Austin A30) started from cold first turn by giving full choke and no accelerator. Then the instant it fired and was running I put the choke in to about 1/2, blip the accelerator so that the engine catches and idles nicely, then ease the choke in more, as much as it will take but still idling smoothly.
On pulling away, especially if up a gradient, it may need a second's quick pull on the choke just to give a burst of richness, and then off. No more choke needed, unless on a very cold icy morning it may need a fraction of choke briefly if I have to stop at a junction within the first half mile.
I have had trouble with needle valves ever since they started improving them. The old all-brass type were fine, but the rubber-tipped ones tend to stick shut sometimes, and there is no proper way of adjusting the fuel level. I've just replaced one that wasn't cutting off properly, letting the float ride too high. Looking through a box of spares I found they weren't even all of the same length. Obviously the valve has to be fully shut off before the float touches the chamber lid.