Can I add rolls of unfaced insulation to increase the R value of my attic insulation?
Yes you can. Every bit helps, though you can eventually reach a point of diminishing returns. You're not there yet :)

I would leave the floor boards to avoid compressing the cellulose. I don't need to tell you to maintain a ventilation path from the soffit vents, but it's worth mentioning. I would also consider building a storage platform for both containers and on which to walk (crawl?) so the ceiling can be fully insulated even under the storage area.