Which type of accredited doctorate would best support seminary adjunct teaching?

I am a senior pastor with about fifteen years of ministry experience, and I already teach Bible, theology, ministry, and biblical counseling courses online for several small Christian colleges and seminaries. I would like to become more competitive for dependable online adjunct positions at accredited Bible colleges and seminaries.

I have an accredited M.Div. and M.A. from Liberty Baptist Theological Seminary. I also hold a Ph.D. and a Doctor of Practical Theology from unaccredited institutions. In addition to my pastoral experience, I have written several ministry books, developed online courses, and earned multiple biblical counseling certifications.

Theologically, I am a conservative Baptist and Calvinistic in my understanding of salvation, though I would not describe myself as confessionally Reformed. I would primarily seek opportunities at conservative Baptist or broadly evangelical institutions whose doctrinal statements I can affirm.

I am currently enrolled in the Theology and Ministry Th.D. program at Kairos University. Kairos has institutional accreditation through the Higher Learning Commission and theological accreditation through ATS. The program fits my ministry and research interests well, but completing it will cost considerably more than some other accredited options.

I am trying to determine whether the Kairos Th.D. would offer a meaningful advantage over a less expensive accredited D.Min. or Ed.D. Some alternative programs are offered by institutions accredited through TRACS or ABHE rather than an HLC-accredited institution that also holds ATS accreditation.

I am not trying to leave pastoral ministry or pursue a full-time research career. My goal is to continue pastoring while teaching undergraduate or graduate courses in Bible, theology, pastoral ministry, or biblical counseling.

For those familiar with seminary education or faculty hiring, would an accredited D.Min. or Ed.D. remove essentially the same credential obstacle as the Kairos Th.D.? How much practical difference do the degree designation, the reputation of the institution, and the particular accreditor make when seminaries and Bible colleges hire adjunct faculty?

I would appreciate candid counsel, especially from anyone who has reviewed faculty credentials, participated in adjunct hiring, or faced a similar decision.