Mark, I think you had a couple of things that together might have caused your problem:
1. Hard snow- by what you described the snow must have been hard putting the snowshoe on the angle of the hill but your body had to compensate for gravity and your ankle took the force of the bend causing your foot to twist in the binding and train runner.
1a. Soft snow allows for the foot to make a firm footing at the proper angle of the body, making it easier on the ankle and the foot tract as you would like. Try and find better snow. Sounds dumb I know but instead of following an established trail (hard pack) walk a few feet away (or yards) and the snow is usually better. If you are in an area you know make your own trail, that is the fun of snowshoeing, you can go pretty much where ever you want. Also see angle of approach below
2. The angle of approach, you said you were walking at 90* to the fall line.
2a. If you change the angle of approach your foot will track better. I had this issue last weekend when walking on a steep hill (45 degree +) on hard packed snow 90* to the fall line, my trail runners we not giving me the best support and I knew that if I continued things would get worse for my feet. I changed my approach angle to a 45* up hill approach and did much better. You could go straight up as suggested but unless you have super thighs you won't last long, using the heel lifts helps here.
3. The trail runners don't give a lot of support when traversing a slope (though I like the flexibility over a boot). If there are no other options and all you can walk on is hard pack, and walking 90* to the slope then boots might be a better option.
Other thoughts, on the MSR's the loose side of the binding strap goes on the outside. It shouldn't make a difference for you runners though, maybe try and tighten them up a little and see how they work, or even loosen them up (along with changing them way you walk).
This might all be a bunch of hyper-bull and I am totally wrong with what you were experiencing, but it also might help.