Disclaimer: science does not doprovide artificial gravity
Remark about your tags: you want to bend space time to your liking. Alas, there is no actual science based way to do that, like there is no FTL travel. There is only science fiction about artificial gravity. The centrifugal solution is the only one plausible in a science-based way.
Suppose artificial gravity could have a limited range
Your opening: "The more realistic ships use centrifugal force for this but mine uses the good old "handwavium" to generate its gravity."
Voilà.. You could circumvent the whole issue with "extra" mass influencing everything else, by letting your folks develop an artificial gravitational field with a limited range. It will not affect the space-time gradient far away, it would be felt only inside the anti-gravity container, withwhere your ship either hangs, or levitates.
Mount things outside
You'll have to mount the propulsion outside on the 1km construct, firmly mounted somewhere on the hull of the container. Inside the container, where your ship is, the gravitational field generated would make propulsion a waste of energy. Your ship could hover inside, and e.g. not feel deadly acceleration of the entire construct.
You need the shuttles to be mounted outside too.. provide for an elevator or a bridge, to enter the shuttles from the ship.