But didn’t the ship spend some of it’s time out of warp drive and within the normal laws of physics?
Never. Space is extremely dangerous, and filled with massive amounts of energy and radiation. Every ship, no matter how small, operates within forcefield bubbles of various kinds to protect it from EM radiation, scalar and gravitic forces, etc. To lose your force field protection is to die a quick death, even if you are a battleship.
Still wouldn’t matter - for every gripe you can come up with for why inertia would make them all Jelly I can invent some gizmo that prevents it by fiat. That’s the wonderful thing about FICTION! ;-)