In order to keep the feel and look of the original quilt, I would be tempted to use wool batting (Hobbs wool is what I would choose). Wool is the elite of quilt battings, easy to hand or machine quilt, and gives good definition without puffiness. I would consider doing a combination of machine and hand quilting. Maybe machine SITD to secure the blocks and hand quilt around (and inside) the embroidered designs. Use fine thread to do a medium-sized background fill in the white spaces around the embroidery.
Was there sashing in the original quilt? I would be tempted to add sashing to frame the blocks.