Fun project. You might be interested in belt presses - they can be hooked directly to the grinder reducing the time (and labor) of moving the pulp to the press. They also allow the whole process to run continuously.
These are neat! I've been vaguely aware of them, but never looked into them too much. It's hard to find DIY plans online for that sort of thing, and I'm not sure I'd be able design my own from scratch well enough to be worthwhile.
In a similar vein, swap out the grinder for a shredder/wood chipper-type model. You will no longer have to cut the apples open, and you can fill it by the bucket rather than one-by-one. Much higher throughput.
To clarify, with the grinder I built described in the post, I did not have to cut open apples by hand any longer. It could shred apples as quickly as apples could be put on the ramp.
Just finished looking into these more. While they seem really neat, even if I home-built one it would be way out of my price range. Just the filter belts alone would cost more than this entire project did.