In addition to what's been said, here's some other things to think about:
If you haven't checked it in awhile, check the compression just to be sure. With that cam and CR, you're probably in the 175ish range, but it's more important that it's consistent. If it's off, re-torque the head and then check it again (we see a lot of people change head gaskets when they just needed to re-torque the head and adjust the valves). Then go through a valve adjustment. Given that you've got a big cam, you might be having some issues as those things have big ramps and wear happens fast, even with good oil. Part of your idle issue may be the valve lash--I don't know the specs for that cam, but big cams usually like loose valves (maybe .018-.020") and loose valves really help idle quality even though they clatter a bit more.
Regarding timing, if you've got points, make sure you've got 60 degrees of dwell. Then check the timing and curve with the vacuum disconnected. With that CR and cam, I'd want about 20 degrees BTDC at about 1000RPM and 32 degrees all in around 3000-3500RPM. If you can't get it to idle down to 1000, maybe 22-25 at 2000. If it's got a bad curve, 32 all in is the most important part of the timing. Then reconnect your vac advance (if you have one). It's controversial, but I prefer manifold vacuum to ported vacuum because it improves idle quality. Try it and see if you agree.
I've learned not to touch the carb unless I've done/checked the stuff above.
Then go to your carb. Spray all around with carb clean with the engine running looking for vacuum leaks. As mentioned, HIF throttle shafts usually are okay. Nohome and Jumper have given you great advice about the rest of the carb setup. All I can add is that there is a bi-metallic compensator in HIFs that sometimes causes troubles and other times the enrichment (aka choke) O-ring will be bad. Either will make erratic performance. We also see more sunk floats in HIFs than HSs or HDs. If the jet isn't close to the bridge (within 2ish turns), that's also an issue--either it's set wrong or the needle is way wrong.
Regarding having to use the choke: The first 2/3 of the choke should only change the idle and the last 1/3 richens the mixture. If you can figure out if the choke is just opening the throttle more or actually richening the mixture, that will help your troubleshooting. I usually set the chokes to raise the idle to about 1800 RPM in that first 2/3. Once you get to the last 1/3, the idle speed usually goes down a bit unless the engine is dead cold.
I'd think with that cam and CR, if all is good, you should be able to get it to idle around 1000-1200RPM. Of course, I'm in Michigan and you're at a higher elevation, so my advice may not work very well at your altitude.