Now about the Defiant: Her being a warship doesn't matter at all. It would still have a cargo area, and a big shuttlebay. So even though it might be close and crowded for a crew of more than 100 on a longer mission, she would still be able to carry a giant amount of people for a short flight.
Quite so. Although we basically see her canonical shuttlebay in "The Sound of Her Voice" - it's a vertical cylindrar shaft with a floor consisting of sliding doors. Housing evacuees there would be akin to placing them in a grain silo. Cargo holds of appreciable size are not in evidence in the storylines. But the interior is big enough to feature turbolift rather than mere corridor-ladder access, and there are plenty of corridors that could be used for refugee stowage without blocking critical access.
Canonically, the size of the Defiant crew is not known. Backstage design specs say 40 people, but we have to remember that the ship was originally intended to be only about sixty meters long or so. That soon grew to 120, then to the modern backstage size of 170 meters, without anybody bothering to alter the crew size figures. At 170 meters, the ship would be about as big as the Reliant or Kirk's old ship, some dangling bits notwithstanding. And those could accommodate hundreds upon hundreds on long term missions, even though Kirk's ship could at one point sail around with just 200 crew on an operational mission, and could be flown by two cadets and a Monkee when need be.
Timo Saloniemi