Is there insulation on the exterior walls? If not then that seems like the biggest/best single thing to do. I would bet there’s some way they can shoot in some without destroying all the walls but idk.
I don’t see how a mini split, which is generally less efficient than a typical outdoor unit, helps at all.
Spray foam insulation is another thing to investigate for the attic.
Also, and this is outside the box, what about planting some trees to throw shade?