Pie,
I'm not familiar with that particular engine but from your excellent description its sounds like all the rest!

The adjustment opposite the needle valve (by the cable) is indeed the low end idle adjustment. The other one (with the spring ) is the "throttle stop" adjustment. If you screw that in and out SLOWLY while moving the throttle arm open and shut, you'll get a feel for what it does. You want it set so that it stops the barrel right when its shut all the way. That would be "engine off" position.
Thats what they all do, but as far as adjusting the high and then the low ends, that best left for a thread with the "engines" experts!