Today I went in again to work some more. I was unsure how to attach the wheels to the main frame, so I reached out to Paul Gregg, a backyard rollercoaster enthusiast and engineer (he also has his own blog and youtube channel). He was very generous and helpful, and he pointed me towards his two e-books, which have a lot of useful information in them (physics calculations, stress test information, builds, etc.). I decided that the front wheels would have two degrees of freedom (on the z-axis and x-axis), and the back would have only one (on the z-axis). To accommodate the way the wheels needed to move, I had to alter my frame.

(Clarification, not my legs)