Quick update!
I measured the hosel diameter properly they are indeed .370. So I reshafted them using brass shims that I cut to 5/8". I was explained by a well known club fitter that usually, only the first 5/8" of a tapered shaft is actually tapered and the rest is pretty close to .370. The installation went very smoothly. I used Golfworks quick center to make sure the shaft and shims were properly placed and used a 24h epoxy.

Have played about 10 rounds so far and the results are great so far. The Ci7 heads with the KBS shafts is a great combo for me. Could not be happier.

Thanks for your help.