This Suzuki has been hiding it's whole life. Picked up a service manual and did the following. Cleaned the carb, new spark plug, valve adjustment, checked timing is good, sealed leaking valve cover, checked cam chain, new fuel line, inspected vacuum line and breather hose, cleaned air filter and a runs a bit better. The idle and air/fuel adjustments do nothing. I have it 2 3/8 out. Has a slight back fire. I now rebuilt the carb with a new kit and still nothing has changed. I've rebuilt a dozen carbs but haven't ran into anything like this. Starts right up with choke, runs good then idles high and back down. After a warm up around the block it idles for about 20 seconds without the choke and then dies. Hmmm.

 

If the mixture and idle screws do nothing, I would suspect your pilot jet is still blocked. Running with the choke on (which circumvents the pilot sorta/kinda) tends to confirm this.
...that's my guess, anyway....
Beautiful Quad! Barn find?

 

I first cleaned the old pilot jet then afterwards cleaned out the gas tank but didn't run a fuel filter. I then installed all new carb parts. Same results. Yep barn find. An actual find from inside a barn . Thanks!

 

Use it! A bike that has stood isn't going to run perfect, and many bikes don't like being left idling anyway. The more you use it the better it will run.