sounds a lot like what happen to my 67ii. first, check to see, with no film in the camera, what the slowest shutter speed you can use before it gets stuck. sync speed is a good place to start. sounds like you kinda did that, but i would run thru all the speeds if you can including bulb.
in that generation of pentax mf cameras and later, according to the guy who repaired mine, they used a lot of magnets and they can develop issues. with my camera, any speed slower than the sync speed, which was 1/30, the mirror would lock as the magnets couldn't keep the shutter curtain open. so I feel that if the camera doesn't lock up with speeds faster then the sync speed and locks up at slower speeds, the magnets are a good place to start. Advanced camera repair in portland fixed mine and it was more affordable than i feared.
john