I'm trying to get to the screws under the spindle cap, but they're stuck under it, so I was wondering if getting rid of these screws highlighted would help me to get to those screws
It should be able to slide/rotate on top of the rubber base. It was assembled like that, with the spindle notches lining up with the holes in the base. So something has moved in the meantime to take them out of alignment.
A moderate amount of force might be needed. Eg the amount you can apply with your fingers by holding the top piece with one hand and pushing with the fingers of the other hand on the rubber base to rotate it.
You shouldn't need to grab it with tools / pliers to move it. If you think you need tools, it's better to stop and have a bit more of a think about it before going further.