Also, reverse the circulation direction a couple of times.
IF no pump, then gravity feed hot PBW solution until the pipe is full and let set over night or longer, then flush.
For my plate CFC:
After PBW cleaning I've also forced extra gunk out by connecting silicon hoses to each end of the CFC, one to my faucet (about 40 PSI) and other end pointing into my deep sink in the garage (there will be splatter), pinching the output hose to let the pressure build which may include a weak spot in the hose to bulge a little and then release quickly. I get a strong spit of water and several particles. Then reverse the CFC and do again until the output is clear.
When you say high pressure, how high is it? I wonder if anyone has figured out how to safely connect your type of CFC to a pressure washer!