I'm posting this to the sci.engr.control newsgroup. Please direct any further comments there -- not only will your interesting question be posted for the benefit of all, but you'll get a richer variety of opinions than just mine.
I don't have any information on Z-N tuning on my site.
If your plant were truly 2nd order with no delay then yes, you could increase P to infinite values and you'd never see oscillation. In the real world you don't have to worry about this, because when you push it fast enough anything will show higher order behaviors.
Ignoring that issue for the moment, you can extract plant information using the plant's step response, then doing some curve fitting to get the various parameters you need for Z-N tuning. It's called "open loop" Z-N tuning.
If you're serious about this, check out Astrom-Haggerlund tuning -- Karl Astrom is one of the giants of control theory (at least practical control theory). He was unsatisfied with the tunings he got using Z-N because it often results in an under damped system. He and Haggerlund came up with a similar method that they claim works better than Z-N, and at least gives more conservative results. If I had to use one or the other I'd use Astrom-Haggerlund. Before I used either I'd want to use a system identification/structured design approach.