There is a spring-loaded post at the opposite end of the cone shaped end of the needle. This seemed to stick but when exercised it moved freely but when I retried it the thing flooded again.

I'd get a rebuild kit. I'll bet on the needle or the seat. A hole in the float would also cause this. The seat should be inspected. Grease any O-rings with an O-ring grease when you re-assemble.

Idle mixture limiting caps were placed on engines including car engines to keep people from playing with the mixture, Using the mixture is set on a rebuild only.

The only real way of removing the limiter caps is carb removal and using a drill press. A punch, a drill and a drill stop might work. The idea is to drill the cap so you can insert something to pull it out. The cap is basically a closed off tube with nothing to grab.