Only aspect that makes me uncomfortable is in the preliminary questions it asks if you have the 500hrs and at this moment in time I don't and they make the point of answering honestly blah blah.
I think you have answered your own question, however for the sake of 4wks I would definitely suggest waiting. Have the questions drafted and hit the submit button as soon as you surpass the 500hrs. For reference BA will take your logbook on any selection day.