So, here's the thing. This would indeed solve the timing problem. But I don't see it as "cost-free" for the film for several reasons. First, it locks you into now-established in-universe "rules" about how hyperspace travel and hyperdrives and such work, when the film really isn't that kind of film. Hyperspace is kind of like "travel by map" in Indiana Jones or Muppet movies. It just is a quicker way to move people from A to B without having to accommodate the narrative for the time that it'd actually take. And what you solve in one instance can create problems in another. So, sure, now we can explain that Luke trained for months on Dagobah, while Han and Leia and Chewie hyperslept, but how does that work with what we saw in ANH, where the Falcon jumps from Tatooine to Alderaan in....what, a couple of hours? Maybe a day at most? Again, you can come up with explanations for it (e.g., backup hyperdrive, suped-up sublight engines, yadda yadda) but then that'll inevitably raise other questions (e.g., "Why in any universe where you have actual hyperdrives would you have backup drives? Why would Han need suped-up sublight engines in the first place, and if he has them, why doesn't he use them all the time to outrun everything else?" You end up having to twist yourself in knots to solve the problems you raised by solving the problem you initially created...especially when that "problem" isn't really a problem anyway.
As we've noted, nobody really cares about the "speed of plot" thing. Travel time, the scope and breadth of the galaxy, etc. isn't part of the storytelling of Star Wars. By contrast, look at something like The Hobbit or Lord of the Rings (especially the literary versions) where the size of the world matters for the narrative, both in terms of allowing time for the characters to undergo their own personal and emotional journeys, and to demonstrate just how much bigger the world is than the hobbits initially think when they live in the Shire. (This is also why the same "speed of plot" travel fails to work in The Rings of Power, because we've already established that this world is vast and travel time matters. You see similar issues in the latter seasons of Game of Thrones, too.) But within the Star Wars universe, it doesn't actually matter. Yes, it creates kind of a plot hole, but not every plot hole actually matters.
Mmm . . . yeah and no.
That scene that I just spitballed up, I can read it off (in realistic character voices) in about 1 minute. And that's with a couple of jokes in there. The cost (in slowing down the movie with tech) is very small to cover one of the movie's biggest plot holes. It's not out of bounds for the franchise at all.
Maybe you'd wanna include another 30-second scene where they are roused from hibernation when they get near Bespin. No need for any real techy stuff there.
It works to explain that Luke was on Dagobah for a while. Otherwise that is not clarified and we don't really see weeks/months worth of activity between him and Yoda. A person who doesn't know SW could watch ESB and think it was a matter of days. It's SW experience/hindsight for us to think it was longer because Luke was established to be so Jedi-like by the early part of ROTJ.
As for it being too much lightspeed tech, I don't see the issue at all. In SW it's established that "jumping to hyperspace' gets you to other planets very quickly. "Sub-light engines" take a long time.
Maybe Han's explanation simply goes: "Well, the Falcon's sub-light engines can get us to Bespin in (insert time here)." That's literally unchanged from the way the movie's logic works now. Those couple of extra sentences about the Falcon's souped-up engines were not critical to the workings of it. I just threw that stuff in there to make it sound like Han Solo talking.
The only tech issue I'm really adding is the concept of emergency hibernation equipment aboard a spaceship. That seems reasonable enough, like a first-aid kit and a life raft on a ship on earth.
Also, it clarifies the idea of human hibernation being possible in SW. That would work forward to help explain to the audience how Han is alive in the carbonite block later. We treat that as a non-issue because we grew up watching movies like this. In 1980 there were probably at least a few more viewers who had a degree of confusion about what was happening when Lando says "He's alive, and in perfect hibernation."
Downside:
If they can use human hibernation in a controlled way for space travel, maybe that takes some of the big-deal out of it. It would make Han's carbonite nap easier to understand but perhaps it would reduce the dramatic punch of it.
Maybe there should have been degrees of it. The Falcon's Bespin trip would be using a light medically-induced coma like they do in real life today. When Han gets carbonited, it would be a scary quasi-death situation.
At any rate, I do think there is value in salting the movie with the idea of a human being 'put to sleep' in some minor way before they do Han's carbon freezing scene. As the movie is now, I've always thought that kinda comes out of left field.
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