Could you post pictures of the, back side, of the old and new switches.
Old switch with the wiring in place.
From your description of the sound the motor makes, the switch & relays are not reversing the power flow to the motor; to operate it in reverse.
I'll keep studying the photos to see if , I can figure out what the manufacturer was trying to accomplish with the three relays.
EDIT: That repair looks like it was a project and a half. Slide drive looks like an early version of a Lippert Venture gear reduction. The newer versions have an overrunning clutch in the gear drive to prevent overloading and burning out the motor, and that clutch will make a ratcheting ( snapping) noise when it reaches it's travel limit.