I definitely put the straight edge on the outside when skinning. Not so sure how much of a difference the side cut makes when traversing on steeps. Seems like I always have an easier time keeping my uphill ski underfoot than the downhill one. A hard boot is definitely going to be a bit better at it than softies. Though things like using the Fuse help with some of this.
Also, the Jones Solution is going to have a Mangne edge on the straight edge of their splits. A mellow cut that is designed to fit together with the other edge. Test results are still out, but it may help at least a little. Neversummer is going to possibly do this with their Vario Grip side cut on next year's splits too. Every little bit helps.