Stop rigidbody A from applying physics to rigidbody B while still allowing collisions between the 2 objects

To avoid going on a tangent, here's the exact problem I want to fix:

We have a spaceship, that has a rigidbody, with gravity switched off (intentional) Items within the ship, such as the player or other loose items, have gravity switched on (intentional) The items within the ship that have gravity, are pushing the ship downward at the force of gravity (not intentional)

So what I want to do is make the forces from the rigidbodies within the ship, such as the player and loose items, to NOT apply forces to the ship's rigidbody. Main things I've tried:

Setting the ship's mass to a high value negated this, but didn't solve it; moreover, having it at that high mass would cause issues later with things like ship collisions with objects outside of the ship, such as an asteroid or another ship

Using Physics.IgnoreCollision, but as expected, that simply makes the objects completely ignore the collision and fall through the floor

Any help would be much appreciated!