which model framework is adequate for path-dependent exotics on precious metals?

to start with, any model you would use for currency options.Then you can go with Cornwall, Hurt, Kentwell (CHK)

It depends what you want. Using a model for fx options would get you started quite quickly (assuming you already have an fx model). The next step would be to use the models in Miltersen and Schwartz (JFQA 1998 p33-59) and in the paper and book by Les Clewlow and Chris Strickland. The next level of complexity would be the model of Crosby. This model seems to be the “state-of-the-art” for modelling commodity options as far as I can see. Links to papers [see 7th Oct] are below. The Crosby model includes the Miltersen + Schwarz and Clewlow + Strickland models as special cases but Crosby also allow for multiple jump processes of different types (amongst other things) which also means you can fit to volatility skews. The point about Crosby, M+S and C+S is they specifically incorporate things like mean reversion and stochastic convenience yields.http://mahd-pc.jims.cam.ac.uk/seminar/2005.html