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
If I were you I'd if get rid of the original spindle with the ball bearing and o-ring retention system, it damages discs. I bought a broken portable CD player online with the spring loaded plastic tabs and swapped them, much gentler on the disc and since the ps1 is only a 2x drive the speeds aren't an issue.