I'd be tempted to floor over rather than fill in, as when you're...er...no longer there, it could be reused?
Also might be useful as a storage facility. I'd guess filling in is more expensive than covering. Assuming that the structure is ok with no water long term?
Either joist hangers fitted to the edge or joists right across?
Is the building ok for insulation?
nor not a Cummings are you?