I don't think I would expect that little lanyard to keep steps in stored position long term. Reworking the landing gear simple but the containment gives me pause.
If you were agreeable to drilling bumper the Stow N Go bracket would work. Though your setup would be a half step too short as it moves pivot to top of bumper. So you'd need a 4th step and flush mount tread to top of bumper height. It would also raise entire stairs stored position several inches so legs wouldn't be issue. Unfortunately additional cost pushes way over had you just picked a 4 step with legs and bracket from get-go.