Carbon among alternative printing processes is especially challenging for a number of reasons, not least of which is the fact that, strictly speaking, it is impossible to print paper white and close highest highlights with continuous tone negatives. A carbon relief is made up of a hardened film of gelatin + pigment. At 0% there can be no film or pigment, as the mechanical nature of the process causes the film to break off at some point before you get to pure paper white.
That does not mean it is impossible to make good prints with carbon transfer, because maximum white is a subjective quality and in most cases absolute paper white is not desirable nor necessary. It does mean, however, that there is very little leeway in contrast for optimum image quality. Too much contrast in the negative or the process and the highlights will begin breaking away somewhere between 5%-10% and 0%. Too little contrast, and the highlights will look dull.
And as Sidney as suggested, this is not a QTR issue, but a process issue. It is possible that this problem could be addressed in QTR with a negative that is continuous tone in the shadows and mid-tones, but increasingly dot in nature in the highlights. But that, if possible, would require a fairly complicated profile.
Sandy