THAT is the pilot either fuel or air screw. In THAT circuit, sounds as it's clogged. You mentioned half a turn to 3 turns, does nothing. That told me it was not working as it should. REMOVE the pilot screw. Spray carb cleaner in there. Spray compressed air in there. Rod the hole out with fishing line or bread tie. Try to seal the hole with your air nozzle to really force the clog out. Research welch plugs on carbs. You might need to remove one or more to get BEHIND them to get the carb clean.
I haven't fired compressed air through there yet but it has had a load of carb cleaner through. I'll also try compressed air in case the carb cleaner hasn't moved something, plus a wire guitar string I've found works well. I've pictured the fuel screw port in the venturi below, what do those three just visible (hard to get phone to focus!) behind do? They're connected to 72 in the diagram via a channel (showing in pic 1 top of carb) in the carb body - again all blasted through with carb cleaner and apparently clear.
The fuel screw was doing little previously, but now if I lean it off too much it stalls, so is working at the least in part.
Flywheel - haven't got in that far yet, will check and also do fins if clogged. Valve clearances likewise.
Will also check float level. Disconnecting the solenoid kills the engine, but I'll check the voltage to see if constant. I'm twisting the carb once it's off the engine to unscrew the bowl, as I can't see a way to easily disconnect the solenoid wiring at the solenoid. Twisting the solenoid will have twisted the wire and stressed the connection over time / previous owners I'm sure.
@Forest#2 was there info missing from my last? I will check tomorrow in daylight again. Noted re welch plugs, thanks for the tip!
Appreciate your continued help!