Great info, Zen Master Ken. I've been digging through my shop manuals, etc. to find some decent photos and/or sketches to help our friends along their journey. No luck yet. Plenty of photos, but none that scan worth spit.
Paragon, you must "enhance your calm." Didn't do a carb rebuild myself until I was about 22. Damn things made me nervous just to look at.

That was more than five years ago.

Okay, okay - it was A LOT MORE than five years ago.
As I said at the beginning of this discussion, the first order of business is to make sure the choke is functioning properly. And, yes, that bulbous black thing-a-ma-jiggy with the two broken screws is a choke coil which has more than just a passing effect on your cold start status.
Get out the carb and choke cleaner and make that fuel and air mixmaster shine. If your linkages (that would be the little rod-looking doo-hickeys

) aren't able to move smoothly and FREELY, you can turn screws until the end of time without ever fixing the problem.
Now that you have cleaned everything and have everything moving freely and have gotten your butterfly to flap her wings a time or two, go do everything Zen Master Ken says. He has much wisdom to impart from his training in the Bowtie Dojo.
You can do this! And, if not, a $45.00/hour specialist can fix whatever you destroy.
"Mind like parachute - only work when open."
Charlie Chan
John