(I'm not sure exactly what the idle jet is, though...)
I think maybe "idle port" is a better term. It's an alternate fuel pathway used when the throttle plates are closed (at idle). It allows a small trickle of fuel to flow into the intake manifold when airflow through the carb is relatively small. This page
has some pictures that give the general idea.
If the idle port is clogged, no fuel at idle and engine dies. If you sprayed everything out with carb cleaner, you're probably OK, but it's something to keep in mind if everything else checks out.
I would buy a vacuum gauge and give your system a check. They're not very expensive and they're very useful for diagnosing problems.
It's a thermal automatic choke, and unfortunately, I can't seem to get it adjusted so that it's fully closed when cold and fully open when hot. ... I don't believe the idle cam is engaging.
If you adjust the choke so it's closed when cold, and manually engage the fast idle cam, does the car start and run smoothly? After it warms up, if you manually hold the choke fully open and disengage the fast idle cam, does it continue to idle smoothly?
If the answer to both questions is yes, then I think your idle ports are fine. The fast idle cam and choke-not-fully-closed problem might impact cold operations, but after warming up I don't think
a slightly closed choke would cause significant problems (slightly = 10 or 15 degrees from vertical). It'll run maybe a little rich but it should run OK.
So if it idles OK when cold (and manually configured for cold operation) and idles OK when warm (also manually configured), but still dies after going from cruise to idle, that makes me go back to vacuum. I had a 1976 Ford (yes Ford) Capri P.O.S. in high school that I could not get to run steady until I tested vacuum at each and every hose. Turned out one of the smaller ones somehow got plugged with gunk and was causing havoc. Looked fine on the outside, but caused problems with smooth running. That was a California car, too, so double the usual number of vacuum hoses for smog.
This is all just general-purpose carb troubleshooting, I'm afraid. My car's in the shop 1500 miles away so I can't provide specifics for Mustang carbs.
Except what I find on the web...