One more option in addition to Erik’s.
If you have multiple clients desiring this, and you want to consider making this a public integration option your clients can use, consider creating an integration on the Okta Integration Network. It will make it easier for your clients to self-service.
But it also allows you a different way to create the API service application where you can use client credentials like you have right now without creating the signed JWT. You can read more about it in the Use API Integrations subheading on this post (I know I sent this to you before, but specifically calling out that subsection)
It’s fairly new, so there are not a lot of docs/tutorials on doing it, but I’ll link in what I have so you can evaluate if this is the right option for your needs.
Dev docs
Product announcement with use case
Let us know how it goes!