I have a similar sticking fire button on my black k1. The white one works fine. The black one sticks if I press on the left side of the button.
I also developed auto-firing today. It turned out that it was the DoggyStyle
rda I was using. The long 510 pin makes it autofire. Hitting the fire button made it read SHORTED. I think the atty is pushing down the pin and hitting the battery + terminal. Maybe a little heat shrink in there will fix it. I just put a different atomizer on it (Taifun gs II) and it is working fine again. I got the DoggyStyle for pocket carrying which the k1 clearly is unsuited for so it isn't a big problem for me.
I opened it up to look at the sticking button. It hangs up on that left edge. I had hoped that filing would fix it but I haven't tried it yet. Your experience leads me to believe that more modifications will be required. I saw that the board was mounted a bit off center. Maybe that is the problem. I may open up the working white one (which doesn't stick and didn't auto-fire but I didn't force the atty down all the way to find out.)