For rawhide backing you can put it on any time. For a wood backing like hickory I like to get the stave to floor tiller stage and be sure the limbs are bending evenly and together so I get a nice even backset after gluing up in Perry Reflex.
Either rawhide or a wood backing would work fine for what you want. You could alse use silk, linen or brown grocery bag paper for backing your ERC. Being that it is a board I would definately back it.