on the tuner page do you see a export as PDF or CSV?
get that(download the CSV), then look up an online csv to json converter
that may be easier than what I did, manually adding the chord and key tags - I had to do trial and error with the special characters. I just did an editor macro to add the chord & key labels & thought I was done, then it took me another half hour to realize there were improperly escaped characters - backspace and quote - "\" and """.
(I hope I haven't misunderstood what's going on here & am offering non sequitur advice)