Do the brakes work? Can you down shift?
You 2 basic choices - continue out the NE corner, and take Chief Joseph to Cody.
'backtrack' to the Lake, and go out the east entrance to Cody.
On the east entrance, you have a slight rise to a pass near the park entrance, and then a steady downhill.
On Chief Joseph you will have a drop to the Beartooth junction, and then a bit more to a scenic canyon crossing (stop to look), and then a climb over a pass and down. You could figure out the actually altitude changes via the contours on Google Maps (terrain mode).
After Cody you have a crossing of the Big Horn Mtns, US16 is usually recommended.
If you want none of that, then consider the north exit to Livingston, and I90 the rest of the way.
