take your s023.iff or whatever stadium you want and extract all the files to a folder.
In blender import the items.SCNE file. THe specific model within this you are most worried about is items_scoretable_geo and I don't know if reflections work but if they do you want to edit items_scoretable_reflection also.
If you look at vertex groups they have their own groups. You can just select those and move them out of the way or scale them to 0 to get rid of them whatever you want.
For the "black cases" do you mean there are really dark shadows in that spot now? If that's what that is you will have to edit the lightmap
See what lightmap the no slip mats use in the items.SCNE
Then find the actual file to make sure you edit the right one
And that's as much as I can help because I don't know how to explain the lightmap files.
I don't get why you are saying these are new or unrealistic because they have been in the game before and you can see them at real games. Plus have you ever played any organized basketball? People do use these things you rip off a layer and then wipe your shoes to get dust off, it is better than using your hand