10mm is enough for for the lifeline, altho you could go more. The Prussic line should be smaller than the mainlne, about 70% from most of what I've read. You will want your mainline to be at least 10 feet longer than your stand height and anchored as high above you as you can reach. My lifelines are 11.5 mm mainline and 7mm prussic cord. There is cord made for prussics, supposedly it grips the mainline better than regular cord.
I've not tried your method of climbing, but please let us know how it works.