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I'd be interesting in developing some greater familiarity with what is/isn't know about the role that modeling can play in what I call below "open-ended transactional inquiry," so will certainly look into Hestenes work.  Probably also relevant is work by Uri Wilensky at the Center for Connected Learning and Computer Modelling at Northwestern (http://ccl.northwestern.edu/netlogo/resources.shtml).

The issue of what is a "model" and how it relates to a "story" is an interesting/important one.  Yes, of course, a "model" as physicist conceive it is a particular kind of story, one told, as you say, with "equations, graphical relationships, or geometrical constructs."  And so part of the problem for physics instruction, as that is currently understood, is how to get students familiar with this particular set of story telling tools.  I certainly agree that without that students "aren't ready to grasp the limitations of the models we are using, let alone create a robust model of their own." 

An interesting question is the extent to which it does or doesn't make sense to try and get students to understand the story of physics using the tools that physicists use as opposed to other story telling tools, but that's a question for you and other physics teachers.  The more general question is what are the advantages of physics type modelling in relation to other kinds of stories, and whether one can keep those advantages without the mathematical particulars.  In equating models and stories I had something of this sort in mind.  What seems to me important about models isn't the particular tools one uses to make them but rather that they are stories with well-defined components and well-defined relations among the components, so one can easily manipulate either and see what the consequences are.  These are, it seems to me, the features that make them good devices for constructing understanding, testing understanding, and creating new constructions.  So, for general purposes, I would call anything with these characteristics a "model" or empirically derived/useful "story."  And I think it would be valuable for educators to help students develop model making, story telling skills along these lines, irrespective of the particular tools used or needed in particular cases.