I'm a bit late to the game here, but just noticed this post and wanted to relate that my Yoki (4 yo F2 male) also has pica. He'll eat anything cloth-like (towels, clothing, shoelaces, oven mitts, our new rug...) and now also most things that are rubbery in texture (luckily not power cords). I think it all started when he was a kitten with wool sucking, which we discouraged, but later developed into a more general cloth addiction. It can be a real headache, but aside from trying to distract him with play and wear him out a bit, there's really not a lot we can do. We've told the vet and the vet agree's we're feeding him adequately as well, which rules that out. (..though by nature he is the hungriest creature I've ever seen. He's always begging for food - even after a hearty meal.)
We of course worry a lot for his health, since having all this synthetic material in him can't be good. So far he's either passed it all fine into the toilet or vomited what he eats somewhere in the house. I feel we have been lucky in this.
At this point we have come to terms with it and simply know which things to keep out of his environment to keep him safe (and to keep us from not getting furious at him). It's not ideal because we're constantly scanning for anything he'd like that was left lying around by mistake. By now Yoki has me conditioned so much that even at someone else's house I'll get a fright at first if I see a t-shirt or towel just lying around.
Anyway, sorry that my post may not be of much help, but pica is difficult to treat and there's no real cure that I know of. I just wanted to commiserate with you, so you know you're not alone.