Sounds like to me that you have an HEI unit dropping out under load, which I see quite often on several brands of engines. And it may not effect the same module all the time. Normally I find on Kaw that when one is acting up with a little testing you will find that both are going goofy. I have engines that will run on the other cylinder when you ground out one plug, and it doesn't matter which plug, which will make both of them seem normal. Neither plug will fire through a spark tester, and if you unplug one spark plug wire and try to start the engine to get it to run on the GOOD cylinder it won't fire. And it doesn't matter which plug, which indicates that both modules are not producing correct output at cranking speed.
And as far as valve adjustment unless they are hydraulic valve lifters they are adjustable. Some of the Kaw's have a bolt and nut that goes through the rocker arm. that bolt is ascentric and you adjust the clearance by loosing the nut and then turning the bolt, which because it is off center adjust the clearances. and then while holding the bolt retighten the nut. Will take several attempts to get it to the correct clearance.