I am another who clearly remembers Luke missing with his first attempt of the grappling hook in the Death Star chasm. (My memory is that he made good contact on the first attempt, but the hook didn’t catch, so not an air shot.) I originally saw Star Wars at the Glenwood Theatre in Overland Park, KS, from a first-week engagement 35mm Dolby Stereo print. I think I saw it seven times there before I saw it anywhere else. I have recently reviewed this scene both on the Blu-ray Disc and the YouTube video linked below. I’ll refer to the times in the YouTube video as reference of some things I’ve picked up on. Maybe this will give a new perspective on this.

At 1:49: It appears Luke is preparing to throw the grappling hook. This is super quick and can easily be missed, or probably interpreted differently. Watch it a few times and closely watch the movement of his hand, body, face and eyes; and the grappling hook appearing for just an instant. I think the biggest clue is that he looks up intently at his aim point.

At 1:55: Luke begins unspooling the grappling hook line from the stormtrooper utility belt he is wearing. It is quickly clear that he does not already have a loop pulled from the belt at this point, although he was already unreeling and looping it previously.

Between these two we have 5 7/8 seconds (141 frames) of four shots which I believe are inserts.

(13 frames) 0.54 seconds of Luke behind Leia as she fires twice. (a great continuity match for Leia from the previous shot, but not for Luke).
(12 frames) 0.5 second with the shots missing the stormtrooper and him firing back.
(31 frames) 1.29 seconds of the shots missing and Leia firing a single shot back.
(85 frames) 3.54 seconds of a wide shot of the chasm with Luke still unspooling line.

Now watch it again paying careful attention to the music. Then go back to about 1:40 or earlier and listen again without watching (eyes closed if necessary). At 1:50 I hear from the music exactly when Luke makes his first throw. At 1:56 I hear exactly when he begins his second attempt (the start of the second unspooling). That gives him about 5 seconds to reel the line back into the utility belt after he misses, before starting to unreel it again.

This leaves me with two possible theories to explain this. (My opinion is that the first is more likely, and the second likely accounts for others remembering the same thing even though they didn’t see a print from the original engagement.)

A portion, if not all, of the 35 exclusive first-run 35mm Dolby Stereo prints were struck with the 5 7/8 seconds of Luke missing and reeling the line back in. The alteration with the inserts replacing those 5 7/8 seconds was likely made prior to the striking of the 8 70mm Dolby 6-track exclusive first-run prints. It was almost certainly made prior to striking any additional prints, including the 35mm monaural prints. The prints containing the original 5 7/8 seconds were likely never seen again after being returned to the studio. (I think this would fit in perfectly with the George Lucas who never can stop tinkering and never considers his work a finished product for very long, with the changes made between the 70mm and 35mm prints of ESB as an example.)
The combination of the music for the scene combined with what is seen around these 5 7/8 seconds is so suggestive that it has lead many of us to believe that Luke missed, even though we never saw it that way.

John Williams’ music seems so perfectly tailored to, and suggestive of Luke making two grappling attempts that I find it extremely difficult to believe it was any other way when he scored the scene. I think it likely at some point after Williams’ score was complete, Lucas must have decided to cover up the failed attempt. Just my speculation at this point, but I think it may have been to better match the final battle. My understanding is that Luke was intended to have a failed trench run before Marcia Lucas edited it to the form seen in the final movie (apparently and thankfully before it was scored), and George may have decided (just after the last minute) that he wanted Luke’s grappling attempt in the chasm to mirror that change. As the scene is now, it seems like Luke is unspooling enough line to reach the Falcon, or maybe even Yavin. I’d love to see the original assembly again, the one Williams scored. I say again because I do believe I saw it back in 1977.

https://www.youtube.com/watch?v=ECN-Q7tWg8M

I did once read the Alan Dean Foster novel, so it is possible that influenced my memory. However, I don’t have a history of remembering false things about movies I’ve seen. The only other thing I clearly remembered different between Star Wars in the theater in 1977 and when I first saw it again later (on CED Video Disc), is that there was no “Episode IV A New Hope” in 1977, which of course ended up being verified. For the Empire Strikes Back I remembered the hologram for one of the Star Destroyer captains conferring with Vader disappearing immediately after an asteroid is shown striking the bridge. That of course was never visible in the pan and scan home video releases and I was always disapointed it wasn’t there, probably one of the reasons I’m an original aspect ratio advocate.