Perhaps nobody understands your question. Bradford6 gave you some good pointers and it seems from your demo that you understand how to compute a rotation about one axis.
"However, I can't figure out how to find the x and y positions of a given point while playing with all three of the rotations at once."
- I don't understand your question - would you care to rephrase it?
"However, I can't figure out how to find the x and y positions of a given point while playing with all three of the rotations at once."
- I don't understand your question - would you care to rephrase it?