If you have spongy, rotting areas, you will probably need to saw back or cut down past the rotted areas, but if you can wait another couple of weeks before doing it, that would give the plants more chance of recovery. Check the trunks right down to the base for signs of rotting, oozing, and particularly orange gunk coming out, or white spit leaking - cut down beyond those points, wherever they are. Then wait - you may find they shoot new growth from the remaining trunks, or from the base, or both, but this may not happen before June - if they only shoot from the base, you can remove the upper part of any trunk left.