Is there a JSON-based genomic feature format? There's a variety of formats for storing genomic features (e.g. Genbank, GFF, GTF, Bedfile) but all of the ones that I'm familiar with use either a custom format (Genbank) or a CSV with defined column conventions and space for additional data (GFF, GTF, Bedfile).

Is there a feature format that is JSON based and adheres to a defined schema?
JVCF is a JSON schema for describing genetic variants. BioJSON is a JSON schema for multiple sequence alignments. The output of mygene.info's gene annotation web service is JSON-formatted. 

You might build one of your own schemas from any or all of these, as inspiration for structure and content. 

Consider that most genomics formats are historically tabular, because they are not hierarchical, because they originated prior to the advent of JavaScript as a common programming language (and subsequent use of JSON to serialize data), and because a lot of stream-oriented UNIX tools read in data and process it in ways that are natural to tabular structure.

Some tabular results can be hierarchical, but use inefficiencies in field values to apply hierarchy. JSON is inefficient for storing tabular data, but it is absolutely wonderful for hierarchical data. This difference is perhaps worth considering.

One could think of storing a gene as a master object containing various haplotypes, exons, introns, features, associated variants, associated TF binding sites, gene ontologies, etc. Ordering or prioritization of such items would be possible with the use of sorted lists within a gene object. The format is as extensible as it is a matter of adding a property, list, or object to the schema. 

To gain adoption or "buy-in", build tools which publish it to users, and tools that consume what users get in order to do things, along with conversion and validation utilities.