January/Feb, those seem to be when I have time to do my wiring. Not so much fear of dieback, but bud damage. I've seen what can happen when you more or less loose most of the years leaves. It can set you back a couple seasons. So slow and steady is best, and be very careful of fert in spring before leaf harden. Wind protection is paramount in the spring as well. (course most of this is based on EU beech, could be that others are less picky.) I have a J.Red Beech as well, and it seems to be a little stronger growth habit, but it's also younger...
And when I state not being able to do as much, I also am meaning things like defoliating, and some types of pruning to incite budding in the season.
Sorry for hijack B!