I've always calibrated negative exposure and development using my favorite printing paper. Of necessity, this has changed over time. Nevertheless, the "calibration" has remained essentially the same, which would indicate that the different papers I calibrated to were not that different. I like fiber-base glossy, white base, neutral tone paper. Possibly, if I used matte paper or warm-tone or whatever, the calibration would be somewhat different. Still, I tend to think that the differences in paper when calibrating are likely not as much of a variable as conditions in the field when shooting (variances in luminance range from that calibrated, metering, etc.). I guess what I'm saying is that the approach of targeting specific negative densities for particular "Zones" is likely a viable method as long as some general idea of how the end tones will be reproduced in the print is taken into account. I can't imagine that the Zone System was developed any other way, so, basically, the printing paper was being taken into account from the very beginning; the values one gets from Adams and others for targets were not just arbitrarily chosen.
I still use the visual method using proper proofs and my current favorite paper(s) to determine and refine exposure and development. But there is inherent inaccuracy in calibrating and even more variation in the field. I spend a lot of time printing on a different grade/contrast setting than that calibrated to, despite careful calibration. My goal is simply to get close enough to my calibration that I can handle any discrepancies with the contrast-adjustment tools I have at hand in the darkroom. I rarely have an "unprintable" negative, which tells me that my calibration has done its job.
My use of the Zone System is primarily to be able to visualize what a final print from a given scene would look like under several different scenarios and then choose one that suits my purposes or decide not to make the photograph in the first place. Determining exposure and development of the negative is important, but secondary.
Best,
Doremus