I haven't done a deep dive into K60, but if anything like Praktisix where shutter / mirror box / film transport can be unbolted and lifted free from an outer "exoskeleton", it would give you much better access to the camera's inner workings. Shutter drums and rollers can be cleaned and lubed with the aid of a light oil diluted in solvent and applied with a syringe but avoid getting oil on the ribbons or rubberized fabric. Mirror box also likely needs attention. Supposedly, original factory lubricants were high-spec stuff, but they weren't aging well in the 1990s, let alone three decades hence.
Although it may be very tempting to fiddle with the shutter tension adjustments ("just a little bit more..."), I'd leave those alone for now, and concentrate on reducing friction.