oh geeze, I found the bug that pulls it to the right.
The rocket physics is pretty basic. I don't do anything hand-rolled. Its just a rigidbody physics object that I apply some force to and let the physics engine handle the rest. But, I also applied a constant force to it so the player doesn't slow down too much for the longer levels. The problem is, I forgot to rotate that constant force in the direction of travel. It doesn't fix the determinism, but its still something.
Awesome! Thanks for your help!