what method are you using to make your stacks? putting a drop of juice on the stack and sliding your fingers down the stack to spread it out can really help it to want to stay together while you are working on it. i like to fold mine in half too (if you need 8 plies, cut 4 piece of wire that are twice as long as your finished wire needs to be, + an extra inch or two for the drill chuck/swivel end). that bend makes it pretty easy to get the ribbon stacked, and its a bit sturdier than the opened end of the stack, so its a good place to start wrapping/binding/gluing. once that end is tight, set up a ribbon slider there and slide it towards the open end. it should straighten out the rest of the ribbon and keep it all parallel while you bind/glue that end and stick it in your drill, folded side to the swivels, then the slider is right there waiting for you to do your wraps and slide it back to the swivel end.
that kind of prep can also help with round wire aliens/claptons, or anything with 3+ round wire cores (glue/bind the end once you get it parallel, install a ribbon slider, slide it to the other end and glue/bind it when its all tight)...or slide it half way down, install another slider and slide that one to the end, so you have a middle stabilizer as well.