Sweet! So, as far as I can tell the visual issue tends to happens whenever one planet is set to be orbiting another planet, but only if they aren't also set as a satellite (although that can cause issues with overlapping name tags but that's fine) - it looks like they remain as satellites correctly in orbit around their parent planet (side note, if it's possible and doesn't screw up other things, setting the cloned planets to being satellites might be something to look at) - although it can just happen without it being a planet orbitting another planet
so to list the ones I've found and their issues: (my suspicion for most of these is that's its due to the mod setting the orbit as being around a certain object, but ICF changes that to instead be orbiting the sun, causing it to change positions but remain in the correct "formation, if that makes sense)
Metal and Star: when adding compat to any of the actual planets (Mirandus has no surface and as such needs no compat) the planets move to being substatiantially (visually) farther away from their intended location - any planet that I didn't add compat to remained in the correct location. In addition, just having intercontinental Rocketry enabled without modifying it moves the Stargate's location and I have no clue why
Secretas & Frozeta: weirdly enough, the opposite problem from M&S - when adding compat, Secretas (the gas giant with no surface that I didn't add compat for) move to a wildly incorrect location, while Frozeta remains where it should be
Muluna/Terra Palus: I haven't been able to replicate it anymore with muluna so I suspect some combo of mods I have might've been causing this one, but Terra Palus still does it - they're supposed to be moons in close orbit of their parent planet, but instead they're in a completely incorrect location.
Dea Dia System: same problem as Metal and Stars, the planets to which I add compatibility are in a very incorrect position
All the Starmap Nexuz planets that I have enabled (maraxsis, arrakis, corrundum, janus, tiber, tenebris prime, naufulglebunusilo): this one is actually probably the easiest fix - they have compat code in their mod that fixes the ones that were already in ICF when they released or made their compat but all the extra ones I added were I think adding their cloned planets to their original position in the solar system instead of their updated Nexuz location - easy enough to fix through adding in the compat for the extra planets into their compat though (although there's one other weirdness and that's the angle of the clones, but I assume that's probably harder to fix since nexuz doesn't give them a new object to orbit but instead just moves their locations out to far away and displays an image underneath to pretend they're orbiting a new system)
That's also not going into the absolute mess that is caused by also attempting to use organized solar system/redrawn space connections/cosmic social distancing (I think a decent amount of those issues would be fixed if you could define the planets as satellites of the originals since innately those mods ignore satellites when redrawing paths/changing distance from host planet but there's other issues with this that wouldn't be fixed, mainly that for some reason some planets(mainly satellites it appears) have their clones appear directly underneath them even though both this mod and cosmic social distancing should stop that from happening and some of the clones dont appear to have their tiers so they end up in the basic tier 0 location, in a line under the sun) (there's also the potential that having this mod load after those so it gets the updated locations of the planets could solve some of the issues)
Sorry for the long post lmao, figured giving you as much information as I've been able to discover might help you find a clean solution. Let me know if I can help with anything.