Case has stated on their own forum, their CV (which they term as a 'modified 1095') is hardened a couple RC points beyond their stainless 'Tru-Sharp' steel. Their stainless is taken to RC 55-57 or so (they've published this); this would imply their CV is taken to RC 57 at least, or maybe a little more. No reason to worry about it being too soft.
All the issues I've seen in sharpening my own CV blades, is that some will need some thinning at/behind the edge to really pop hairs and perform at their best. Edge angles at or below 15° per side (30° inclusive) are the best target; I prefer an edge around 25° inclusive (12.5° per side). Over time, in resharpening mine, I've also noticed edge retention improve with a few subsequent resharpenings. This could be a sign of some heat-damaged steel on the factory edge, which is weak and will need to come off.
And the stones & tools used to sharpen CV don't need to be anything special. A simple, two-sided SiC or AlOx stone, of the type found at ACE or Sears, will do great with these knives. The 'fine' side of the stone will finish it to around ~320-grit or so, which is a great working edge on CV. I'd prefer anything between 320-600 for CV. A medium Arkansas stone also works well for the finished edge on CV. Use all of these stones with some mineral oil.
Regarding the edge produced on the ceramic tube/insulator, it's likely that edge had a burr folding over. That'll account for the sharpness deteriorating quickly from that one. It's common with ceramic rod/tube-type sharpeners; I generally avoid using those. They're very hard, load up too fast and focus pressure into a very small portion of the edge; and that's basically a 'perfect storm', burr-forming trifecta, right there.
David