I commend you for your foresight in searching for an apartment compatible with building a sukka. I'm still not sure if I understand the situation precisely, and it may be helpful if you could email a photo of the porch.
Let me give a little background and see if that helps clarify the issues. There are 3 qualifications for sechach to be Kosher. It must grow from the ground, as opposed to metal, glass or plastic. It must not be an object capable of becoming tamei such as food or a vessel with a receptacle. It must not be attached to the ground, as opposed to a tree branch that has not been severed. Furthermore, a roof that is used the entire year is not valid for a sukka, even if it meets all 3 criteria. If you would screw down the slats, they would become comparable to the tree branch and would be lacking in the third condition. It would not help to loosen just a few slats, because the remaining ones would be invalid as if they were made from metal. It also does not help to avoid sitting under the screws, because the problem is not the screws themselves but the slats which they would render pasul. That is why I recommended placing a couple of 2x4s on top of the slats to hold them down. Their weight should make the sukka safe but not create an issue of being attached.