Does it makes sense to publish new math whose primary significance is its applicability to another field?

I'm an applied mathematician and I have written some papers with a focus similar to what you describe:

• They don't include fundamentally new mathematics
• They achieve new/faster/better results in some application, by applying mathematical techniques that are not known in the application field

This kind of work should usually be published in a journal of the application area, not a mathematics journal. The application specialists are the ones who need to learn about what you've done, so they can use it. You need to write your manuscript in a way that is accessible and convincing to application specialists. This probably means not focusing on theorems and proofs, but on results. It may require changing the vocabulary and notation you use. It is often not easy, and you will need to spend time reading the literature of the application field. It can be very helpful to find someone in that field you can talk to, or even get as a co-author.

My strategy is to first publish this mathematical method of function fitting, in a math journal, so that it gets some authenticity and help me get some serious attention from [anonymized topic] experts for providing labs/infrastructure or attract venture capitalists for a startup.

You have contradicting goals:

• If you want to sell some service or software based on your idea, then you shouldn't publish it. Once published, your method is available to everyone so you don't have exclusivity anymore. Instead you might want to license it, but for this you probably want to setup a company first and get legal advice from a professional.
• Otherwise there's a wide range of [anonymized topic] journals and conferences where you can submit. You should be able to justify your method, typically by comparing it to state of the art methods and demonstrating that it outperforms them or overcomes some problems they have. It's more convincing if you can demonstrate its usefulness with some real application, but if you have solid arguments about its potential applications then demonstrating the theory might be accepted as a contribution.

In both cases the main question is not about high dimension or not, it's about which kind of problem it can solve better than state of the art methods.