[postfacto]

Perhaps agile doesn’t actually work (despite the hype) and your team having this quandry is actually your team starting to be awakened to the truth of why agile tends to cripple any project it touches.

Dump agile, write the backend first, in a thick juicy horizontal slice, create a decent json schema document for it that you show to important people at the mandatory demo, and then hand the schema document to the front-end person with the understand you may have iterate on your API a bit as you incorporate their feedback.