That's a 235 carburetor, but if that is really a 51 size jet it is no wonder at all why you need your choke on to keep the engine running and why it sputters and stops without the choke halfway engaged. That is a small jet and will cause the carburetor to run pretty lean to very lean. 58 size was a common jet back when we had real gas. 59 or so might be better with ethanol. Your power piston does appear bent...straighten it, please or it may stick and hang up in your power valve opening. Which would interestingly cause you to run too rich or...if the bent piston was causing the power valve never to engage, you would be running way too lean when you needed power.
However, the 58, 59 jets were for the 235 and not for the 261 (but you don't have the right carburetor for the 261 so just changing to a much larger jet might or might not help you).
Last edited by Jon G; 08/13/2023 3:25 PM.