There's no realistic alternative to loading the next system in a hyperjump.
It took me literally 3 seconds to figure out an alternative. All with using existing tech. Here we go:
You set a target on a Galmap, it appears on your HUD. Max range for that option is limited to 2k LYs. You can set ANY location as destination, provided it's within 2k LYs radius. Then you engage hyperdrive and jump.
Now - interdiction-type minigame starts. As we know, star's gravity field makes you drop into real space. So while in hyperspace you need to avoid gravity fields. Your nav comp will help you with that task providing safe "route vector". Your job is to actively keep that vector point in front of your ship. The longer you stay on target, the farther you will jump.
Failing on staying on target results in drop into real space. Either premature drop or you get to your destination, game during exit part would calculate where you dropped.
Then you would determine where you are, what star type it is, what's in the system and what's nearby. And you could see how much off the course you are. For refuelling purpose single and direct jump would work as current jump. Target nearest OBAFGKM star, align and jump there (single jump within your FSD range). Anything further than that - hyperspace minigame.
This way we could be actually surprised by the system we exit and people would share epic stories about new record of single jump distance. For jumping whole 2k LYs would be really hard. The longer you are in the minigame, the more difficult it is to stay on course and chances of premature drop are ever rising.
Pro-active, entertaining and fun.
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You want to explore traditional way - use single jump feature and crawl through space as we do currently.
You want to get to the other side of the galaxy in a few hours instead of days? Use FarJump.