Sorry to hear about the damage.

A pic could not hurt.

Otherwise I'd probably wait till May and do the trimming.

I have seen trees really pull through but on their own time.

its kind of hard to see from the picture. Start at the trunk where the burlap wrap is and trace it upward, though the dead branch kind of gets lost. I dont suspect the whole tree will die, but it’s very lopsided without that branch. I’m mostly wondering if it will ever even out on that side.