Adding pressure to a heatsink won't improve its cooling efficiency or capability, and in fact might cause more harm than good.
Your fan was working harder/faster before because the inside of your PS4 was so dirty. The dirt caused an airflow restriction, so removing the dirt would require less effort on the part of the fan.
How are you determining that it's an overheating problem? What temperature are you measuring and how are you measuring it?
When you added the washers to the heatsink (!!!), did you lift/wobble/otherwise break the connection between the heatsink and the processor, even a little? And if so, did you clean the heatsink and processor and apply new thermal compound before reassembling? If you separated the heatsink and processor, and/or if you didn't clean/reapply new compound, you likely have a thermal break between the processor and heatsink.