To be fair, we've never really known how hyperspace works. The films don't say a thing about it. The dialogue seems to conflate "hyperspace" with "lightspeed" although it's not entirely clear. The passage of time also isn't clear in most of the films, with only TLJ suggesting a specific 18 hr window in which everything can/must happen....but then does nothing to clarify how hyperspace works to ensure people know you're still playing by the universe's built-in rules (or consciously breaking them). We don't have a 24-style ticking clock, so we don't know how long it takes for anything to happen, or even necessarily all of the sequence of events and how they play out (although sequencing is a bit easier to figure, given a few common points where storylines intersect).
But that's always been true for Star Wars. None of that stuff has been explained. Things happen and ships travel at the speed of plot. Night and day fall at the speed of plot and ambience. None of it is really clear.
For example, on the fuel issue, the suggestion is that the ship is running out of whatever fuel it uses to propel itself in regular sublight space. We don't know if the hyperdrive runs on a different fuel source, or even if it runs on fuel at all. We don't know if Kylo's attack on the ship blew up some critical fuel reserve or whathaveyou. The whole thing is a mystery.
For the most part, I'm ok with that. I don't expect a lot more in my Star Wars, even if I might prefer it if it is better explained. I tend to think it's harder to work that stuff into a film without breaking the 4th wall, though. And if your focus is on the experience of the characters and their level of knowledge, going into detail specifically for the audience's sake is a waste of time if it would be reasonable to assume that everyone IN the movie universe would know what's going on.
Here's how I'd fix the chase:
1. Decide on your pace. Do you want it fast, or do you want it slow? I think the film wanted slow, ominous, creeping doom. And it got that...but I think it could've done so even with a sense of speed. Set it against a backdrop with something really large in the far background, and smaller things up close. The large thing can stay static. The smaller things can whiz by to give you a sense of speed in spite of the creeping doom. Speed plus slow gaining would work.
2. Explicitly show Kylo's attack crippling some critical propulsion equipment. Coolant lines, hyperdrive fluid, sublight engine regulators, whatever. Lampshade it. "The hangar explosion took out one of the regulators. We've rigged a backup, but I don't know how long it'll last if we keep burning at this speed. Admiral, whatever you have planned, I hope you can pull it off quickly, because our engine could blow any time now.
3. Show the stakes. The film tried to do this somewhat, but they could've handled it better. Some nameless ship has its engines go dark and gets blowed up. Who cares? It's only a model. In another case, they had a ship captain on holo screen flicker out of existence. Again, who cares? He's some random dude who pops up on Space Skype, says "Godspeed!" and winks out of existence as another model explodes. Instead of that, take me inside the bridge with him. Show the explosion around him. You know why anyone remembers Porkins? Because we saw what happened to him. We didn't hear him scream over the comms and then get static. We watched him die, and that gave the entire sequence stakes. All of the pilots as they get picked off in the Trench Run sequence are humanized, given a moment, and then engulfed in flames. That creates real stakes. It shows the cost in a real way, not in some remote, detached way. Nobody remembers Red Leader's first wingman who got blown up. Why? Right. We didn't get an interior cockpit explosion sequence. If we had? There'd be a wiki page to that pilot and probably 3 novels from the Bantam-Spectra days of the EU! Give me more of that with the TLJ space chase. Showcase another ship's engines explode, killing an engineer, and then have someone vidcom to the bridge to scream "Captain!! Our regulator's just blown and it took out the chief with it! We're dead in space!!!" Then show the captain's reaction of horror or grim acknowledgment as he realizes what's going to come, cut to the interior of the Supremacy, and have a smug Hux issue a "You may fire when ready." Close-up of the enormous cannon firing, switch to the shot streaking towards the ship, fast-cut to the interior of the ship and we watch it blow up around everyone, then cut to the bridge of the Raddus (or wherever on the ship) and watch Laura Dern looking steely but clearly moved, while Poe loses his ******. Then later, when she has the troops all come to the Raddus (only to offload them later), showcase one of the closer escort ships scrambling to get everyone on the shuttle, the shuttle launching in time, and then cut to the bridge of the ship to show the captain calling the Raddus and saying his "Godspeed, Rebels!" line, then show a similar sequence. Shot from the Supremacy, shot hits the ship, fireball on the bridge, captain screams, quick cut to the Raddus' bridge as we watch the people there react and the tension builds.
Doing this would have the effect of (A) imbuing the entire sequence with real tension and dread, (B) show the effects of that on the tension and dread on the Raddus' crew, and (C) make it clear that Poe is driven to his stupid move not simply because he's being a dick, but because he's cracking under the pressure (sort of). If Poe's arc is about thinking strategically instead of tactically, then you accomplish that by having him react to the obvious thing in front of him, without thinking through the longer-term options or implications of his merely reactive solution.