My experience with braiding and pasture is not a good one. In the interests of saving time, I braided my two horses I was taking to a show the night before and then turned them out in their pasture. Come the morning, the mare was fine but the gelding had evidently been eating through the fence and had rubbed his braids out taking most of his mane with them - in places there wasn't enough left to braid.
So, if you're training the mane to one side, I wonder if you couldn't slick the mane down with hair gel and leave it that - that would be safer than braiding it? The other alternative, rather than doing a complete braid, after you get troublesome bits brushed over to the proper side, perhaps just band them with a couple of strategically placed rubber bands and leave it at that - that should reduce the risk of a braid catching and the hair being pulled out plus with the bands should break/give first reducing possible damage.