Hello G,
"You are getting warmer". Clean the valve rocker cover off. there will be a set of numbers stamped into the top (unless someone has had it off and now it is installed upside down) These numbers provide the B&S engine information only.
That label under the hood is a convenient common replacement parts and accessory label that Craftsman riders typically have.
There is a Chassis product information label usually under the seat on the chassis or affixed to the seat bottom, Craftsman also tended to place them at the very rear or on the side of the frame.
Your initial problem description indicates a possible fuel restriction such as in the fuel tank pick up tube, or fuel nipple fitting. Bugs, dirt and old grass clippings tend to populate in those. It creates this kind of running and stalling out issue.
Next suspect item is the spark plug. If it came from an online source, throw it away and put a correct parts store Champion or NGK plug in it.
Last idea that comes to mind for the moment is possible water in the fuel.