I'm very familiar with this issue and here's my take on it.
when i first started making soap, i was still earning terminology at the same time. i did not know that at first, i was making liquid soap using a CP method. That process takes longer to trace, and as you mentioned, it achieves a transparent soap. But also most importantly, it doesn't neutralize as fast as HP does. After buying Catherne Fallor's book on liquid soap making, I started heating my oils hotter. Overall my soapscooked faster and because I let them cook overnight on the warm setting on my crock, which is about 160*, there was never any need to worry about neutralizing. Going back to CP, if you let your soap cook for minimum of 3 hours...or overnight if you can, you'll achieve the same neutralization. So you're only other "problem' would be getting to trace, because KOH traces slower than NaOH, from my understanding. I don't make solid soaps, so I can't say for certain. If you still want to gain a transparent soap using a CP method, add a little bit of alcohol to the final diluted batch and let it sequester for a few days. If it doesn't clear up after say..3 days..add a little more alcohol and let it sit for a few more. If no clarity by then, well, that's it. It probably won't clear up. Or it might, and will just take a little longer.
