I don't like the storms at all. They're uninteresting mechanics; if they were occasional areas of peril we had to go around, they'd be all right.
As it was (previously) they were too random and could occasionally wreck a fleet, without feeling like a good mechanic... the current version feels like we're pinballs, it's also random, but usually not fleet-wrecking.
Honestly, I don't think Hyperspace works. Alex has tried about 5 different iterations now, and they're all pretty boring examples of Travel in RPGs that aren't inherently rewarding or interesting.
How to fix?
1. Make it difficult / perilous to get from Point A to Point B; hard-to-dodge enemy swarms, deadly storms (that aren't random blippy things, more like multi-week affairs so we can go around them reliably).
2. When we get to B, make it easy (in terms of our time on this planet, at least) to get back to A. Perhaps, if A and B are pretty close to one another, it could open a "warp tunnel" that re-connects this System to the other one, permanently, for example; then there's no more need for Hyperspace and we can move efficiently.
And gosh darnit, have the ability to build Gates to connect two areas, so that Travel is less of a drag on our playing-time. When I found myself keeping my high-speed setting for Burn after playing that way for a day... it was a sign that, frankly, travel's not that interesting, despite Alex trying to put in things to make it so, like the occasional hostile Scavengers or Distress Calls that don't give enough reward to be worth responding to. Honestly, I'd rather have a trip that was scary-dangerous, but was relatively short, time-wise, and where I didn't have to do it a million times.
The issues I see with instantaneous transport or really quick transport would have implications for the player's interactions with the very simple economy that has been implemented. It becomes very easy and fast to go from surplus to deficit planets, requiring a rework of the economy, possibly turning that kind of credit making option off. Its maybe not a crazy idea, but it would require a fair amount of balancing work with the other subsystems of the game.
Secondly, hard to dodge enemy swarms is probably not the best option. What is scary for a fleet composed of frigates is not scary for a fleet of capitals, so that hard to dodge enemy swarms would have to scale in some way. As for someone who plays a fair bit of iron man spacer starts, whats worse than boring travel, is getting caught having to do the boring run away battle every, which takes far longer than the travel time usually. Presumably sufficiently large fleets would simply find it an annoyance being constantly interrupted by a swarm of non-dangerous fleets.
As for deadly storms, that sounds like just a variation on what storms we currently have (or used to have). As a iron man player, I'd prefer not to lose a several hour long session to a mis-click on the travel map, which is not to say I haven't done that and accidentally engaged something I shouldn't have, but at least that is due to a fleet and has some interaction after the mis-click. If storms are literally deadly and will destroy your fleet that is probably reload time for most players - which feels terrible to me.
Similarly, lore-wise, it becomes hard to justify raiding fleets giving you time to respond in transit, or even intercept them in transit with your transponder off when quick travel is an option. They should launch, and then just like you can, be in the target system efficiently.
I'm not sure what the right answer is. I don't think the campaign layer is intended to be the main draw of the game, but it also should be fun when you're there. Its a mini-game between sessions of the main draw of the game, the space battle simulator. On the other hand, it seems like people prefer the campaign mode to the stand alone missions. Presumably because its a framing device that lets you tell a story, rather than just disconnected battles.
I'm guessing for testing our variations on your concept, it should be possible to create a mod where when you reach a jump-point in system, instead of taking you to hyperspace, it just presents you options like:
1) Travel to a core system
2) Travel to an explored system
3) Travel to an unexplored system
and then a sub-list like
1) Askonia (5.0 ly, 50 fuel, 20 supplies)
2) Corvas (9.0 ly, 90 fuel, 36 supplies)
3) etc
6) previous page
7) next page
And then teleports you to a jump point of that system less the fuel and supplies, and perhaps some damage if you didn't have enough fuel/supplies. Not sure how hard that would be to code up, but as long as the system list can be parsed, and there is a change fleet position function (which the jump points presumably normally use), it shouldn't be too bad I think.