If you need to access these sites for work, I suggest requesting them sequentially. Generally, people don’t adjust filters until people complain. After you become the number one ticket creator for mundane site requests, they’ll usually bend the rules for you or learn to adjust the policy.
The reality is that people who create these filter policies often do so with very little thought, and sans complaints, they don’t know what their impact is.
If your company actually does this, that's impressive. The vast major Big corporates that I have seen do not even really review these requests unless they come from a high-ranking person. When they do actually review them, it's usually a cursory glance or even just a quick lookup of the category that their web filters have it on, followed by a rapid and uninformed decision to deny the request. Oftentimes they won't even read the justification written by the employee before they deny the request.
God help you if you need something that's not tcp on port 443. Yes, I'm still a little bit bitter, but I have spent a lot of time explaining the difference between TCP and UDP to IT guys who have little interest in actually understanding it, and ultimately won't understand it and will just deny the request. Sometimes after conferring with another IT person who informs them that UDP is insecure and/or unsafe, just like anything, not on Port 443.
The reality is that people who create these filter policies often do so with very little thought, and sans complaints, they don’t know what their impact is.