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.