Curious if it is possible via some configuration to prevent Adjusted Sector from generating systems right in the core, almost on top of other core worlds.
This is with the standard core systems, not random generation.
As an example, I've got generated systems almost on top of Galatea and Samarra, which is a bit strange: https://imgur.com/BKEEQKV
Edited to add the image link.
You may want to play around with the settings, the default ones tend to result in this. If the constellation area is large enough it will extend a close constellation's potential area over the core. Even when you get a good balance, a gen may still put constellations close enough to the core that they'll infringe on the outermost core systems added by mods.
I've had luck with
"AdjustedSectorConstellationCount":150,
"AdjustedSectorConstellationSize":1500,
"AdjustedSectorConstellationCellSize":10,
These create a sector with just over 300 systems at normal sector size or just less than 700 systems when the width and height are increased 50% (compared to around 500 under normal adjusted sector settings and around 170 in vanilla) with a core overlap only about 1 in 4 times, and only on the outermost ones added by mods. Then make small incremental changes and see if makes something that works for you.
You'll probably wanna turn down some of the features like ruins and remnant just a little too, if you stick with the normal sector dimensions. Just follow the guidelines on feature number vs the number of constellations and there shouldn't be any weirdness.