Hey y'all, I'm nearly 'bout to lose my mind or what's left of it.
I Have a '63 Valiant 225cid. It will start cold at the snap of the key but give it 5-10 mins and it just dies unless I hold the butterfly mostly closed.
The carb is the Carter BBS with a fresh rebuild as well as a new choke pull-down.
As far as I can TELL the stove choke is free and working fine. The Butterfly is near shut when cold and then opens as it warms and then it dies. I think I'm starting to repeat myself. See? I'm losing it.
A couple of questions as I don't have a factory manual in front of me....
Am I correct in assuming that the stove choke spring pushes the rod out to close the butterfly when cold allowing it to then release the pressure on the butterfly when warm?
The pull-off holds vacuum but I can't get any action from it on the lever once the stove loosens and gravity drops the weight (fast idle lever).
I only have 2 hands and the left one's kinda retarded and I would love some insight into this.
That, or a driveby while my head's under the hood.
Either would be a great assistance!

It sounds like there's nothing wrong with the choke; you can stop focusing on it. The problem happens once the choke is no longer active, which means you've probably got a problem with the idle circuit in your carburetor -- fresh rebuild or no fresh rebuild. It could be a missing curb/hot idle speed adjusting screw, or that screw is backed off way too far. It could be a piece of trash stuck in the idle circuit blocking fuel, so try as described here. It could be just a badly misadjusted idle mixture, which should be adjusted as described below the links to carburetor operation and repair manuals in this thread. It could even be unrelated to the carburetor—if the valve adjustment is too tight, you can get a failure to idle when hot, but that's less likely than a carburetor-related problem. And more generally, tune-up parts and technique suggestions in this thread.

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Too many people who were born on third base actually believe they've hit a triple.

Okay Dan, Thanks for stepping in with an assist.
First off, I see only one hole on the front of the throat, and it does in fact come out the idle screw hole. Is the second hole of which you speak that very tiny in the middle of the rod that runs from front to back with that hole pointing towards the rear/ linkage?

The two holes mentioned in that other post are on a Holley 1920. On a Carter BBS, you've got the one angled hole at the front of the carb throat (it does not come out from the idle screw, which is down at the base of the carburetor in the throttle body), and the other much smaller hole in the middle of the bar that runs front-to-back in the carb throat.

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一期一会
Too many people who were born on third base actually believe they've hit a triple.

Funny thing. It's amazing how well this thing'll idle with the jet-idle screw properly poked out clean.
She's been running kinda just fine since I've corrected that.
I can get it dialed in from here with not too much effort Dan.
May I offer you a happy song by Taj Mahal as a sign of my most generous gratitude to being there to share your business with me.
Cheers!

(Taj Mahal - Ain't Nobody's Business But My Own)
( https://www.youtube.com/watch?v=7gzVL3zHxdU )