sure sounds like you have fuel delivery problems.. Rust and stuff collects on bikes in storage. Some of it breaks free and clogs up a filter or something. Since your bike runs better choked, it indicates a lack of fuel. Perhaps the float is low but i suspect fuel starvation from a clogged-something.
the carb is only a small part of the fuel flow circuit. Clean the rest of it.. all the way up to the gas cap... filters, screens, everything.