A shop put my cage in with the headliner in. I don't know how they got it all welded up because it's right against the headliner. I would think headliner out would be the way to go.
What they do is cut holes in the floor, slip the bars down, weld the upper part of the cage, then bring it up to height, and weld the bottoms. It's the way to go here since, dude wants a headliner and a cage.