If you are near Scott's Park, you are about 2 miles from Red Hill. You really are very unlikely to get a place there, although, as it's a big school, you might get casual places throughout the year.
Are you far from either Elmstead Wood Station, or Sundridge Park? Each of these is only one stop away from Grove Park, which is about half a mile from Launcelot Road, which is where I think you said they currently are? Two 10 min walks, with a short rail journey wouldn't be that bad, and trains go direct from Grove Park to Cannon St, so easy for you to get to work, then.
You could stick with it, and move them if places came up. But you might have to consider accepting one place at a time, bearing in mind that if you have one child at a school, their sibling is automatically boosted up the waiting list. (Doesn't guarantee a place, of course.)
Or have I got completely the wrong end of the stick?