Conjecture on periodic orbits in no-slip billiards with external force

A no-slip billiard is a billiard system in which collisions with the boundary exchange tangential and normal velocity according to the no-slip collision rule. An accessible point is a point of the table that can be reached by a billiard trajectory. A path-reversing periodic orbit retraces its path after a collision. A wedge is the region between two intersecting boundary rays.

Periodic-orbit conjecture. For a no-slip billiard with an external force, $2$-periodic non-path-reversing orbits exist between any two accessible points on an arbitrary table, and isolated higher-order periodic orbits exist between accessible points on a wedge.

These are experimentally suggested possibilities extending the known family of path-reversing $2$-periodic orbits; the source does not establish either assertion.