Incredibly high speed tweening/enemy movement

I've been working on an infinite runner game that runs at absurdly high speeds as a practice project, heavily inspired by the 3rd level in the SNES game Sparkster though remade in 3D with a third-person camera. However I've been unable to figure out a good way to get enemies to have a set path to wander/hover in front of the player at a fixed forward rate. Currently I'm using a floating origin script to reset all objects in the level back to the world origin when they wander too far away, so I'm sure that'll be an issue with this, but as of now I've yet to find a good solution to my initial problem.

Ideally I would like for the enemy to wander in from off-screen somewhere, and then begin an infinite loop of wandering back-and-forth/up-and-down once it's reached its path, but most tweening/waypoint systems I've seen rely on stationary paths. Advice and tips would be appreciated.