I think your steps should be as follows, taking in mind effort and costs.
1. Remove and reseat heat sink with new thermal paste.
2. New CPU cooler - Hyper 212+ @ R280
3. New case - CM RC334 @ R399
1. Remove and reseat heat sink with new thermal paste.
2. New CPU cooler - Hyper 212+ @ R280
3. New case - CM RC334 @ R399