Edit: As of v 1.3.1 Breeze now DOES support inheritance.
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With respect to Breeze, you are correct that it does not (yet) support inheritance. That is on the Breeze road map and you might want to vote it up.
It does support the ASP.NET Web API and JSON. Curious that you thought otherwise, given that almost all BreezeJS samples are Web API samples that rely exclusively on the JSON content type.