Being "edge aware" is something that I think arrives naturally with familiarity with your knife (knives). Whether working on the farm or "flowing" with combat scenarios at speed that didn't go as planned, I find myself rolling/flipping/reversing the knife as needed to accomplish the task.
With the exception of back-cutting type motions, I think it best to plan on having a single edged knife and train that way, because that is what you will probably have access to or be attacked with.
On another semi-related tangent to the tangent we are on, I teach and practice the use of a knife in reverse grip, but point out to everyone that with the exception of "ice picking" type motions, all of our motor memory with knives is in a forward (usually sabre) grip. Whether you are slicing open boxes, cutting a steak, or chopping brush with a machete, we humans work almost exclusively with a forward grip. Our entire motor memory structure from the time Mom first stuck a knife in our hand to cut that first pork chop to when Dad taught us to whittle and clean a deer, it has been forward grip all the way...
And while I am at it, one of the better pieces of kit developed and issued lately has been the OKC-3S Bayonet for the Marines. Decent utility blade, helluva bayonet, and not bad for a small bowie. I like it and am proud to have had the opportunity to participate in the testing process. Beats the hell out of carrying a "Ka-Bar" AND an M7.
Dan
We just finished teaching a little session in the last Dallas siminar on the reverse grip (edge-in) and saber (edge-up) that offer some very good promise. I introduced in Dallas.....but it make a neat little eye-opener that can get really nasty.