The 300th speed setting is normally hard to cock; it has an extra high speed spring in the shutter.
Shutter blades are probably glued down with old oil and grease. It only takes a tiny bit on the surfaces to stick them together solidly.
This is what I would do; others would disagree, you make your choice.
Unscrew and remove the front and back lens elements. You will probably need a cheap lens spanner to remove the rear element. You can try to clean the shutter with the rear element in place, but it's a pain and the dirt and oil from the shutter will migrate to that rear element, requiring you to clean it from the front with the lens set on "B" once you get the shutter to open and close. Not ideal, but you can do it.
With the front lens element off, wet a cotton bud/ QTip with Naptha and gently wipe the intersections of the leaf shutter blades where they overlap. Don't flood it, just apply enough to start penetrating the overlap. Cock the shutter and place it somewhere above a 60th of a second and try to fire the shutter. If the blades don't move, wipe the entire surface of the shutter blades with naptha; again don't flood it.
Be patient; it should eventually fire BUT it may fire and stick open or partially open. Don't panic.
Continue to wipe around the opening of the shutter or on whatever exposed blades are there with naptha and fire the shutter. Change the cotton bud frequently and run the shutter speed selector up and down in the mid-range of the available speeds. The blades will eventually start to move. Each time it fires, wipe down the surface of the blades carefully, being mindful of the edges of the blades. Wipe in a direction that doesn't lift or bump up against the shutter blade edges. You should start seeing light brown oil come off on your cotton buds.
If you have removed the rear lens element, clean front and back surfaces of the blades. This works a lot better than just cleaning the front, as the dirt/oil will simply move to the back and greatly extend the cleaning process.
If you get frustrated, set the camera to one side and go do something else. You cannot rush this.
Once the blades appear to be functioning correctly for the most part, the slower speeds may still stick, find a speed that the shutter seems to fire fairly reliably and continue cleaning. Start alternating with 91/99% alcohol and naptha and start moving down in the shutter speed range. Should it ever hang, try going back up in speed on the shutter until it fires again and start over. It takes time but eventually it should start firing regularly on all speeds.
Once the shutter appears to be working properly, set it on "B", take a cable release and lock the shutter open. Carefully clean the rear element with alcohol followed with window cleaner.
Leave the front lens element out (after releasing the shutter from "B") and let it dry completely.
Exercise the shutter. If anything sticks, do it all over again.