Not idling right shuts off after giving it gas

This vehicle listed above is all original 258 engine with a carter carburetor. The vehicle was sitting for three years before I got it, but it was kept up with before that. I replaced the battery, starter, fuel filter, oil, and changed out the gas. Sprayed the vacuum line a with carburetor cleaner. No leaks. Cleaned out the Venturi tubes ran sea foam through the carburetor and gas tank and tried adjusting the air fuel mixture screw to no avail. It runs and drives but it idles around 1000 rpm. When I run the rpm's up to 3000 and let off it just shuts off. When I start it after that it will not run unless I give it gas. I am not sure where to check next. I want to keep it as close to original as possible but I will try anything to get her running right. I have no emissions testing in my state for vehicle this old. Limited tools but I can get them. Just not sure what I need. Please help.