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Does FeedPress support JSON Feed?
Experimental JSON support is live on FeedPress.
JSON feed is generated every time the XML feed is refreshed so it’s not a replication from the source, it’s a creation. it currently handles podcasts on RSS and Atom and validates.
You can append ?format=json to the end of your feed URL (no leading slash before the parameter).
E..g., https://podcast.hologramradio.org/master?format=json

Update: As of May 31, 2017, the feed_url paramter has been added. As per JSON Feed spec documentation, it's highly recommended:
feed_url (optional but strongly recommended, string) is the URL of the feed, and serves as the unique identifier for the feed. As with home_page_url, this should be considered required for feeds on the public web.
To make your FeedPress based JSON FEED discoverable in a browser, add a <link> tag to the <head> tag of your website. An example follows.
<link rel="alternate" title="My Feed Title" type="application/json" href="https://feedpress.me/myfeedname?format=json" />