I have a problem with "harsh" definition in general. I never really found out what it means, as it seems to vary from person to person.
Is it just bright, or do you hear/measure some type of distortion/phasing/smearing in high end?
I've made several circuit options with several diferent tubes and ct12, but never found that certain tube makes a mic harsher. I used various russian tubes.
One thing to have in mind is that ct12 is pretty bright capsule. It should be, c12 is a bright mic. However that high end is very, very nice. And very different compared to bright k67 capsules. Both boosted and attenuated it has silky character, it's never abrasive, pointy for lack of better term. It's centered at abouk 8k which i find to be very musical point.
I remember trying it for the first time on vocals, without any backing track. I thought it was waaaay too bright. I was a bit puzzled. But then i introduced backing track, and found out the vocal didn't need any eq treatment at all. It has just the perfect amount of everything. Sometimes i just use hpf, and that's it.
People like u87s and u47s for their "warmth", but then end up boosting hell lot of high end to make those work in mix, not the case with ck12 mics.
Could it be the same thing you are experiencing?