REST: Historical work remaining by date

I'd like to use the REST API to return data for a historical burndown for a set of issues. So ideally, I would supply a JQL query (and possibly a start date e.g. beginning of project) and it would return data to allow me to construct a table of total work remaining (Remaining Estimate) by day:

Date Total      Work Remaining
2017-06-01    5,000d
2017-06-02    4,950d
2017-06-03    4,900d
2017-06-04    4,850d
... (to today)

I don't need individual stats per issue, although that would be okay if that was the only way. I see that I can use rest/api/2/search with fields and changelog params set to "changelog", then hunt for and calculate changes to Remaining using created/field/from/to fields, but that seems like a lot of unneccesary data to download over the length of a project. Can I specify in JQL that I only want the changelog.histories.created field and only changelog items within that where changelog.histories.items.field = timeestimate or status?

TimeTracking data looks useful, but I can't see how to get it historically, only for current snapshot. Or is there another REST-accessible source for this kind of data - the Jira client's Burndown report has the right data, but doesn't show history. It seems like the kind of data that would be very popular - I know I won't be the first to ask this, but I couldn't find an exact equivalent question (https://community.atlassian.com/t5/Questions/Tracking-quot-Remaining-Estimate-quot-changes-via-Rest/qaq-p/310296 is close.)

Any ideas?

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