Re: Not an antique, but I need some help.

[Don]

OK, so you just got the engine, it wouldn’t run because the float needle was stuck closed, correct? So, you really don’t know the engine’s history or how it ran for the previous owner. You have checked compression and it is good.
First, on their best day, these engines were very cold blooded. The love to sneeze/fart/cough during warm up and are tough to keep running without tickling the choke. So, please don’t expect this engine to idle like an 18hp from the 50s. The initial needle setting for the carb is 1.75 turns out from gently seated. It is real tough to get a consistent idle from these engines, trying to smooth the idle out by leaning the needle usually results in a lean spit, you usually have to leave the adjustment slightly rich to avoid the lean spit.
You mention that the engine won’t idle, but runs OK at higher speeds. If this is the case, a plugged/restricted high speed jet seems unlikely. In any event, you need the special tool to remove it to avoid damage. If you don’t have the tool, simply remove the bowl and carb drain plug, then just look through the jet by shining a strong mini light down the bowl nozzle. Spray some carb cleaner through the jet, then run a small pipe cleaner through it. The felt on the pipe cleaner will show gum/crud when removed from the jet, avoid poking through the jet with wires/drill bits. I think I hear you saying that richening the needle has no effect at all on the idle quality/sneezing. I know you said you had the core plug out, so I will "asssssume" the low speed needle is in good shape and not broken off in the idle pocket passage.
This carb does not have the conventional packing nut/washers to seal the low speed needle. These carbs have a plastic "retainer" (29) that holds the needle from turning and helps seal the needle. Some of the carbs on the larger engines had a plastic cup seal around the needle as well, but it doesn’t look like this style carb has that seal.
I guess I am getting ahead of myself here though, are you sure the carb butterfly is closing fully, not jammed/binding? Is the carb/timing synced properly? This engine will not idle if the butterfly is partially open at idle. If you have the carb off, look in at the butterfly from behind the carb, make sure it is closing fully, not binding, and has not been messed with. Do not attempt to remove the butterfly or loosen the retaining screws. Did someone misadjust that "economizer" linkage, perhaps that is holding the butterfly open slightly at idle. The other thing to keep in mind is these engines won’t idle if they are running cold, especially in cold weather, probably not much of an issue now during the hot summer though.
Like others have said, sometimes ignition problems disguise themselves and sound like fuel problems. This engine should be able to jump a half inch gap on the spark tester while cranking. There isn’t much that can affect ignition timing at idle. I suppose the flywheel key could be sheared leaving the spark retarded, wouldn’t be my first guess though. Does it look like someone has been messing with the flywheel nut?
Finally, the idle speed on this engine is controlled by the plastic spring loaded idle set screw located on the vertical throttle gear under the engine pan. Is the spring loaded screw in place? Can you move it? Keep in mind that the throttle settings called out on the plastic collar under the twist grip are rarely accurate. In other words, don’t worry if the engine won’t idle much below the start/shift throttle settings, as long as the idle speed is low enough and idle quality is "acceptable". Trying to dial the idle in and make it idle on the "slow" setting will be frustrating and normally not possible.