Employ a shred of critical thinking and realize this app probably drives more value to Yelp than the cost to run the API, and flag it for an exception.
Customer service or sales people like that are usually at the lowest point on the totem pole. It’s likely that they have zero leeway, either you’re gonna pay exorbitantly or you’re out. It’s an institutional problem.
In that case it's not customer service but a customer firewall. If the CS employees are not empowered to induce solutions even if they benefit both the customers and the company then they are literally useless.
And yes, many companies have "customer service" like that designed to waste your time until you go away. That doesn't mean it's the only possible way.
Employ a shred of critical thinking and realize this app probably drives more value to Yelp than the cost to run the API, and flag it for an exception.