zenemek's comment reminded me that you should probably check out the control of the injection pump. I don't know anything about the LK models but assuming the engine is like the older CK/DK models:
Engine power is controlled by the amount of fuel injected into the cylinders. The injection pump has a rack which moves forward to inject more fuel and aft for less. There is a spring unit behind the injection pump that pushes the rack forward such that it rests against a "lever" that moves to regulate engine power. This lever is pulled forward (more power) by a spring connected to the hand and foot "throttles" and pushed aft by a centrifugal governor which pushes harder as RPM increases. The result is a system that produces a certain RPM for each throttle position that is nearly constant regardless of engine load.
So it would be good to verify that the injection pump rack can travel the full distance without binding or sticking. Also verify that the "lever" goes full forward at zero RPM and that the throttle springs (two, I think) are correctly attached to the lever assembly. I think your tractor has a manual stop lever on a removable plate which can be removed to view the injection rack pin and the IP control mechanism. This may be difficult if you don't have a "good" working tractor for comparison.
By the way, Kioti engines changed from an stop solenoid on the right side (external linkages) to one on the front of the engine (with no external linkages) during 2005-2008 with different models changing at different times. I don't know which version you have. But several of the early (2005-2008) models with the new configuration experienced broken teeth on the injection pump gears that control the amount of fuel injected. The broken pieces can effect the injection pump in odd ways, like jamming it in the off position or a jamming it in a high power position. I suppose it could also limit the forward travel of the rack, which would limit power.
Finally. it might help if you gave more examples and details of your symptoms. For example, when you say slow and stop, what exactly is happening? Does the engine die? Do RPMs wind down in proportion to forward speed? At first this was a problem in two highest gears; all gears now? It sounds like a fuel flow problem. If there is no restriction check the lift pump (small pump upstream of filter). It's a simple pump but check valves could be stuck, the diaphragm could be cracked. You should be able to measure a couple PSI fuel pressure out of that pump as you crank the engine.