The cork rings ARE the friction discs and should be soaked over night before installation so they are thoroughly saturated with oil. The pressure from the springs will try and keep the the fictions dry form their constant squeezing. So, there is no slippage, partially attributed to lack of oil, but the clutch is also now dragging and putting pressure on the trans and shift components. This is why you clash gears during engagement, and also why disengagement of gears is now problematic (assuming you adjusted the clutch disengagement mechanism correctly).
I urge you to fix the clutch properly, or you'll soon be looking for trans components, gears, shift forks, shift drums etc. All of which require the engine come out of the frame.