>I was told the southdown would just make its way to the top eventually.<
Opposite is true. The more coarse material will always rise to the top over time.
If you can wait on this, I'd seriously consider doing this more slowly. Just removing small portions with water changes. IMO big changes like this are likely to result in unintended poor results, particularly if you have sensitive corals. If you have bullet-proof corals, then go for it.