There has been a bit of theorizing on this matter. "Your Wonderful Parade" on all of the singles I've encountered, has a lower matrix number than "Ticket To Ride". It's as if "Parade" was at one point destined to be the a-side, with "Ticket" as its b-side. The fact that you have a double a-sided WLP promo adds weight to that theory.
I just pulled up the 45 that has 'Your Wonderful Parade' on both sides of the vinyl. The label on one side of the WLP says 'Ticket To Ride' and the flip says 'Your Wonderful Parade', but the actual vinyl plays 'Your Wonderful Parade' on both sides. The 'Ticket' side in the run-out groove is etched with the following: ^78673-X, as well as A&M 1882-15. The flip 'Parade' side reads: A&M 1881-17, with the number '1' written over the '2'. There are no other numbers listed in the run-out groove on that side.
Hope this helps.