Pike won't spool you. If the carp is big enough it will. I don't know anything about spey casting either, but if you have a fly line, why would you need a running line? It is my understanding that you only use a running line if you are using a shooting head system. And then again some shooting heads come with their own running line. I guess if it were me, I would google up spey casting and tackle used and see what they recommend for a reel. Most reels will tell you how much backing you'll need for the size line you will be using. Also I would go to some of the fly line websites and look at what they have to offer in a spey line. Rio comes to mind.
Dave
" If a man is truly blessed, he returns home from fishing to the best catch of his life." Christopher Armour