.... from Craigslist ad*. It's a 3HP Craftsman and the seller said it didn't
run.

First I pressure-washed the device, to remove the gunk and grass. Next, I
replaced the carb's diaphragm and carb's needle-valve and hosed the dude
down with carb cleaner.

The machine will now run, BUT

If other than full choke, the engine dies.

My skills at small engine repair are at zero (or closely adjacent), so any
helpful hints would be appreciated.

Thanks

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* The owner only wanted ten dollars, so I thought the gamble was worth it.