Well the cross is pretty much freestyle, so you I don't feel there's a standard way of doing it.
Some ways to end up with cross-on-bottom is to just do cross in left or top and just turn upside down, but the looking ahead is harder when you do the entire cube rotation.
Anyway what's wrong with doing double-layer turns? I find U-double layer turns incredibly useful. It's most likely you'll have to do a D layer move anyway for cross.
Unless you align all the cross edge pieces to their side colours first on the top layer, and then execute a half-turn to bring it to the bottom layer. hm.