You could add trim to the perimeter to cover your gaps when closed. Putting your hinges on first under the trim. Opening it towards that back wall (hinges on long side) would give you an anchor point to hold it open.
I've never liked trap doors as they are a pain to keep the doorway clean of...
A better alternative would be 1/2 or 3/4 plywood. If they particle board is at least solid to walk on you could lay the plywood right over top to avoid the extra labor tearing it up as long you can easily locate your floor joists and using longer screws.
If you want to add a little more...