Mine is an LT1000 from 2005, with B&S engine, but I had similar symptoms a decade ago. My manual choke lever would move the cable but the spring in the carburetor was too weak to allow the choke butterfly to return to the "open" position when I manually moved the lever after 5 minutes of running, so mine was running way too rich when warmed up, and would stall out.
Instead of choosing to manually hop out and move the choke with my hand, I installed a 25-cent spring to add more strength to open the choke when I moved the lever from my seated position.