thats where you screwed up.. all spinning spools tell you what diameter line you should have. if it only says 6lb then you only use 6lb. some say 8-12lb so you use 8-12lb... you have a small reel. you need to stick with 6lb diameter line. you doubled it and you payed the price for it. there is a good reason why the put the recommended diameter line on them... you line issues was more than likely caused by line twist. you got line twise due to using the wrong diameter line. hard lesson i had to learn as well. follow this and i promise you will have far less issues with your spin rods..
power braid is good braid for the $$. i have never had an issue with it. i have never had an issue with spider wire too. in fact i have reeled in 80lb water drenched stumps from catfishing with it..
edit:.. if your fireline (the flat) was 6lb on your 6lb spin reel then yeah the shape of it does overlap sometimes. use the power braid it circular. not flat like the others (if my memory serves me)... to be honest what i LOVE to use on spin reels from 4lbs to 8lbs is the Yo Zuri Hybrid... look at the avg break lbs.. the 4-8lbs are the best. the only bad thing is lbs over 8 it starts to get stiffer bc its a hybrid of flouro and something else (cant remember). check this
http://www.alltackle.com/yo_zuri_hybrid.htm