Earl – sorry, not (also!) trying to be difficult, but it’s not possible to do a cross-under turn while “standing still on the flat”. By definition, the board has to move.
Imagine riding your bike and slaloming through a series of bollards. Your head moves more or less in a straight line (along the line of bollards) while your bike moves around a lot underneath you as it goes round alternate sides of the bollards. This is pretty similar to cross-under turns on a snowboard.
You can’t really talk about a “cross-under position” vs a “cross-over position”. The positions may well (in fact, with good posture, should be) more-or-less the same, it’s the movement that’s different.
The turn we teach to beginners is the basic turn. This involves going from sideslipping on one edge to pivotting the board around until it is pointing directly down the fall-line. At this point, you change edge. As you’re pointing straight down, no real speed or balance is required. You then pivot around until sideslipping on the other edge. This is a cross-over turn because the body moves across the board, although it can be quite a subtle movement.