So I've somewhat fixed the issue. I cut the space bar spring slightly shorter and now it seems to work, although it feels a bit mushy.
I did remove the spring from the Windows key on the right side of the space bar to reserve as a "donor" spring since I only ever hit that key accidentally. I ended up not needing it so I put it back, but now that key doesn't work. When the key is attached though, a lot of letter keys don't work even though it doesn't seem like the Windows key ever registered. On another note, the period key now requires a very deep press to register. I'm not sure how everything else started failing like this or how any of it relates to one another.
I suspect some of the switches underneath are going bad because putting the right Windows key on without a spring can still allow me to register it if I hit it hard enough.