It would be very interesting to see the personal dynamic between KF and CJB. I'm guessing there are a number of things about CJ that create doubt in K's mind and that is a very tough hurdle for him to overlook. But K needs to look at him in a balanced manner instead of placing more weight on his concerns.
If K is going to play each game in a close manner, then he should realize that he may be behind at the end of many games and needs an offensive drive to re-take the lead. In such a case, there is no substitute for poise under pressure and CJ has that quality naturally. It's not that JR cannot develop more poise and confidence with experience but his tendency is to over-think each play from the "avoid the mistake" mentality and CJ does not let that enter into his head, at least I have not seen much evidence of that.
Bottom line, this puts K in a quandary because his natural tendency is to play safe, thus JR. I think that is fine, but only if he plays to build sufficient leads and that has been difficult to do with JR. Therefore, I believe the best option now is to go with CJ and please Coach K, don't try to coach away his natural strengths and ability.