I don't know about the rest of the tiller, but I do know something about the GX31. The Honda small engines can run at all position BUT it can't sit on the side or up side down!!!!! VERY IMPORTANT!!!. It has a oil chamber to whip the oil into mist so you can run in all position. But when the engine stop, oil is going to go to the lowest level due to gravity. If the engine sit side way or up side down, oil will sip through the rings and go into the combussion chamber. If you leave it sit long enough, the engine not only hard to start, also it will smoke for a while. But it will clear up. That is the reason the foam filter soak with oil. So do not just tear the engine up until you run more test. You might want to clean the carb. I just did one on my GX31 and is not that hard. But If you can start the engine, I don't think you even need to do that. Just wash the foam filter with soap and water, put oil and put it back. Change the gas filter and check the plug. You check the oil but putting the engine with cylinder upwards, on flat level. Remove the drain plug and make sure the oil just not overflow. Start and let it run for a little while, the smoke should clear up. Then you can continue testing whether it has power. I am not saying the engine has no problem, just say the smoking is normal if the engine sit in wrong position.

" So now I have a clean carb and I know the fuel is at least making it to the carb." don't take this personal, but sort of doubt both comments as facts. From your description: 1) carb cleaning did not entail probing and blowing out with compressed air of ALL carb passageways with small dia stiff brass wire - meaning that a good chance that idle/power fuel circuit(s) are still blocked up. 2) fuel to carb - you did not say how you knew this to be so - did you remove fuel supply line at carb and have assistant crank engine to verify a good stream of fuel being delivered into catch container? Battery - at this point, either put on proper charger or remove/take to shop and have recharged. Surprised engine is still turning over. M/W - remove carb again - disassemble. soak all components overnite in carb cleaner. Using stiff brass small dia wire and Magnifying Glass, probe ALL orifices/passageways in carb components. blow out with compressed air. get everything clean/dry. rebuild using fresh rebuild kit. Do not re-use old gaskets. remount carb. Spray several shots of rattlecan carb cleaner directly into carb throat while assistant is cranking engine. Engine should start or try to start. If only still try to start, still fuel delivery problem, prolly from bad fuel line,filter, pump, etc. If no effort to start, ignition problem. chk for hot spark, ignition switch OK, etc. reply with findings and good luck :)

Disconnect the condenser and coil from the breaker points. With an ohm meter confirm that when the points are open that the meter reads infinity or at least very high resistance (meg ohms)between the engine case and where the coil wire attaches. Then, with the points closed, it should read 0 ohms for a dead short. I've had new points not conduct because they were covered with an invisible oxide film. It took a diamond file to get the oxide off, wet/dry carbide sandpaper wouldn't cut it... Check your condenser with the ohm meter too, from the case to the point where the wire to the points attaches. It may initially read low resistance but should then climb to a high value as it charges. Check the resistance from the coil primary wire to the engine case. It should be very low, perhaps even reading 0 on your meter. There should be a much higher resistance from the secondary (spark plug lead) to the engine case. Coils can be tested for spark with a scooter size 6v battery "dinked" across the primary with the condenser across the primary to absorb the back emf when the battery connection is broken. Careful here since if you get it wrong something along the lines of primitive arc welding will result!

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