Have you made progress with this? I had a similar problem with a KM and didn't get to the bottom of it. I agree with @
MikeMcE, sounds like the problem is most likely up top, during the first part of the cycle. In my case, I could trigger the shutter release if I tried to advance the film (and therefore put some pressure on the cogs) at the same time. I think a lever got bent or something. Anyway, it may be worth sending the camera for an overhaul rather than trying to fix it yourself, before it's too late and you do more harm by accident. IMO, DYI fixes for SLRs are overhyped and it's never mentioned that they're temporary and that the proper fix is never easy. K1000 cameras, like the Spotmatics they inherit the mechanics from, are wonderful if they're serviced properly.