There is a good chance this is your answer.OK, first question, Do you have a torque steer tab right above the prop and do you have it set to the side to correct torque steer? What you are describing as Kick Out sounds like the torque steer tab finally coming clear of the water at that specific speed as the boat rides up higher on the pad. It suddenly clears the water and the force it is putting on the engine is released and you feel a tug to the side. You should also get the same effect to a slightly lesser degree when slowing back down thru that range. You have the engine mounted very low so this corresponds to a higher speed. Raise the engine and it will occur at a slower speed. The torque steer tab is a less than perfect solution and has this drawback. This is why most running a superior steering system like hydraulics remove the tab entirely.
Next is the skittish feeling of this specific engine at higher speed. It is because you have your engine mounted too deep. The foot and housing of this engine is not well hydrodynamic above 45 mph. It starts to oscillate or shake the engine side to side. Yes I know you went deeper to fix the blowout. That is a Band-Aid fix to another problem. You need a prop with more cup and better slip numbers. The laser II has no cup and three blades. It works OK in clean water off certain hulls. Others it looses its grip on the water easily. You need a better prop and raise that engine back up to 4 inches or less under the pad. That will resolve the skittish feeling by getting more of the casing and foot out of the water. A good prop for your standard gear case to allow you to run your engine higher would be the Spitfire X7. This is precisely what I had to do with my engine to correct the same steering issues. Spitfire X7 prop running at 3.5" and steering problems disappeared.