Yea, one of the first things I'm planning on looking at is if Orbital Slingshot interacts with the bonus action attack from Monk Martial Arts. Monk 1 seems like a straightforward dip for this class, especially considering that the two classes are thematically coherent.
I'm a little bummed the class is heavy with reaction abilities, Lodestone Ricochet is a good mechanic to boost overall damage, but it's competing with Harrier's Orbit and Lodestone Shielding (both very valuable defensive abilities) to do so. I think I would be happier with Harrier's Orbit if it just happened automatically after a lodestone attack, no action required. (But keep a bonus action to withdraw.) The 3 lodestone limit keeps the ability in check, already, and 1d4+Wis damage +disadvantage on attacks is only slightly better than the bard's vicious mockery cantrip.
The subclass is a little on the weak side, also. The 3rd level ability is essentially mage hand. The 6th level ability is a portion of Sharpshooter, which I imagine would be a priority feat for Lodestars in a feat-enabled game. The 10' lodestone buzzsaws at level 9 are thematic and interesting tactically, but the heretofore never required Intelligence dependency is odd. Considering how the class has so many abilities restricted by lodestones in orbit, the extra restriction in rounds seems unnecessary. (Adding a general constraint that if you travel more than, say, 300' from a lodestone it travels back to you, or disintegrates would make sense.)
The 13th level ability seems to be T*****'s Floating Disk (edited for OGL compliance

), but with another restriction on usage. Floating Disk is already a ritual, limiting this to a tertiary stat Mod uses per long rest seems cruel at 13th level. Vital Impact at 15th is fine, although another Int dependency is there.
Personally, I have no problem with the subclasses using a new stat (Int certainly fits the thematics of the subclass), but ideally the subclass would be at 1st level if it's going to make a big impact on stat priority. The class already has a mediocre hit die, no built in defensive advantages at low level (other than shield 3-5 time a day, which isn't nothing, I admit), and has to prioritize a mental stat for attacks. It's already straining to get up Wisdom, Dexterity (for AC), and a decent Con, putting in a 4th stat priority is just too painful. Giving a subclass specific bonus to defense based on the subclass stat (I assume it's going to be a different stat for Imaginative and Instinctual) would be appreciated here, I think, so the class can afford to give tertiary consideration to Dexterity.