Have you tried an emissions test? That can tell you a lot about how the combustion is doing, and what you would need to adjust at the carburetor. Have you checked the spark plugs?
unfortunately the most cmmn cause for a bike not starting ff the kick start but starting with a bump is being too low on compression,although to you foot it may feel like enough it does need to be nearly 100% as high as it should be to kickstart.the easiest way to check the condition of the piston is to take the exhaust off and look up the port in the barrel ,it is usually the exhaust side of the piston that gets damaged as it gets hotter.good luck.Adam