Not sure about the cable but to help get the pipes clean .. block the engine end opening and stand them up and fill with a strong mixture of something like simple green or purple cleaner .. one of those good degreasers . I have also read of guys taking the pipes to a shop and paying them to set them in there hot soak tank .
For the carbon. Use a long flexible piece of metal on the header end. Problem is, you can't access the longer portion of the pipes with a rod because of the bulkhead like chambers. And thats where all the carbon would rest. I too would like a better way. You could put round rubber stops used for plumbing at the header ends and fill all the pipes with a degreaser. Like, suggested earlier. But, I think that would take at least a couple of gallons. Unless, someone didn't mind recycling from one pipe to the next.