I'll post some pics tomorrow if you really want them... but in brief, for each adjustment (my carb has 2, but some have 4) there is a boss cast into the baseplate. Each has a welch plug about 5/16" in diameter, installed backwards (lip toward the carb) so I can't just grab it with a screw extractor. Behind the plug is the idle mixture screw, which has a special head, although I've read that the right size Allen wrench will work.
This carb originally came off a '86 or '87 Ford truck, with either a 351W or 460. The primary bowl actually has cast into it, "Manufactured by Holley for Ford". They apparently really went out of their way to make it difficult to change the idle mixture, and I think the plug is actually hardened steel too!
AHH you left out the oddball carb part (ford application)
I would follow some of the previous suggestions and offer a few more
1. if you can find an appropriate size bottoming tap, you may be able to thread the cup enough to "Pull it out" with nuts & spacers.
2. A left handed drill may work
3. Depending on the depthe of the cup, once a hole is in it you may be able to "Roll" it out like a freeze plug.
4. Heating the aluminum with a small butane micro torch and quickly goiing after the plug may work as aluminum expands fairly quickly.
5. carbide tipped cement bits work well on hardened steels and they are dirt cheap. I would STRONGLY recommend using a drill press or mill so you have better control over the feed. You do not want the drill to get pulled in to the adj. screw
Again a few pic's would help
keep us posted
