I also enjoy Sparse galaxy settings for the more strategic pacing, but have noticed the AI can become closed in and doesn't seem to handle it well early. This is especially true on Box/Sparse galaxies. The universe is more Moo2-like when Boxed, however it's discouraging to play for hours and find the last AI on a huge map only to discover he's turtled in some corner the whole game with no outside contact due to one bad jump. I tinkered with giving all ships a base increase (as proposed above) but at that point you're just essentially playing on a non-sparse galaxy, with slower movement.
A better solution IMHO is to increase the range bonus from Warp Lane Amplifiers. This way the key expansions ships (Outposts, Colonies, Scouts) can reach through these RNG map bottlenecks if needed, without throwing off vanilla fleet movement balance. This also creates "frontier" situations where you and your neighbor can both reach systems with Scouts and Outposts, then fight over them, without allowing your main fleet to get involved until the frontier is actually secure.
I doubled Warp Lane Amps (+1 -> +2 parsecs) and have had great results on Box/Sparse galaxies with the AI. It creates some real Star Trek frontier situations, until someone can actually get an outpost up long enough to get a real fleet there to defend it. Scouts fighting Scouts, and lots of strategic maneuvering. As the game goes on, the effect of this settles down since Amps give a flat bonus instead of a %% range increase. Early on +2 is a 66% bonus (as opposed to vanilla +1, 33%) but as each tech with a base fleet range increase is discovered, this bonus begins to diminish.
I honestly think +1.5 for Amps would be perfect since that's a +50% bonus from the start of the game (just like Moo2), but in my test games I just felt like it didn't help the AI enough on Sparse/Box galaxies. I most definitely would NOT use this mod with anything but Sparse galaxies, and I honestly would not recommended it even with Sparse/Elliptical ones. Ellipse galaxies look nice, but even when Sparse it's just too crowded. There are no real "frontiers", and every civilization will discover each other by mid-game.
I'll attach the mod to this post if anyone wants to mess with it. In addition to the Warp Lane Amplifier change, I also reversed functionality of the "Show Range Circles" game option, if it's enabled. Now the maximum empire range is always displayed (e.g. with Amplifiers). If you select to move a ship without a Lane Amplifier it will display that ship's range as a smaller, inner circle. This change lets you see at a glance if there's any frontier you can reach but are not aware of. In vanilla I found I was often paranoid-cycling through my scouts, just to see if there was a reachable star I wasn't unaware of.
There's a readme included with the names of vanilla files modified for each of the effects listed above. You can easily change the +2 bonus to +1.5 if you'd like, or simply delete/remove the Range Circle changes if you don't want to use them.
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