Would people pay for newsapi's alternative?

I don't have any experience with these services, but here are a couple of questions and points that could help you. If they don't, just ignore this comment :-).

1. The 2 services you mention seem quite different in terms of what they offer, at least from looking at their websites. Are they really competitors?
2. newsapi.org seems quite straightforward in terms of product, offering and functionality. Why do they have the pricing they have today?
3. If you can get a sense of market size + can define what it would take to get to feature parity with newsapi.org + can figure out the cost/pricing + can offer it at lower cost, then yes it could be a good idea. But obviously you don't need to figure out everything, you can start small, for example define the core features that a potential customer would pay for (also see point 5!).
4. If you haven't done this already: with a bit of searching I sometimes find blog posts of the people behind the company (often founders, sometimes employees) that write about their experiences or even things like the tech stack they use, how they built out their product etc. That can be helpful in getting an idea of the complexity of the product and its core features, and why they made certain choices.
5. Most importantly: you indicate that you already have clients that give you feedback. This is extremely valuable! You can define the product / feature set together with these potential customers.