When I have worked at a big corp and have integrated with a third-party API, there has always been an 'engagement' with the enterprise company's Professional Se

When I have worked at a big corp and have integrated with a third-party API, there has always been an 'engagement' with the enterprise company's Professional Services/Sales Engineers/??? about a contract and SLA for use of the API. This might get your foot in the door. If you can bring $$$ to the table, that's another helpful approach, even if it's a token offering - $10/mo or whatever at least tells them that you're serious.