This will be long.
First of all, do you actually have any idea what type of work is done on the academic research side of marketing or management? The academic research side of business is nothing at all like what is taught to MBA or graduate certificate students. Read through some recent papers in the top journals in those fields to get an idea of what academic research in those fields actually is. I think you might have some idea of what goes on in the quant side of marketing, but I honestly don't think you have a clue about the behavioral side of marketing or academic research in management and its subfields.
Second, you don't necessarily seem to actually want to do a PhD in marketing or management. Rather it seems that you want to be in academia, so you want to do a PhD in some field and you are using a B-school PhD as an escape from a different field that is in trouble now. Adcoms can usually sniff out that type applicant pretty quickly. Most B-schools have far more qualified applicants than spots and B-school PhD programs typically only matriculate 2-4 students per year per field. You seem bright and motivated, but most top tier, or even top 50 B-schools will likely skip you over for another applicant who seems more interested in their field. A lower tier school might be more willing to take a chance on you.
Third, letters of recommendation are the most important part of any PhD application and the best letters are from people who adcoms will know or recognize. You will not have that, which will hurt you in the application process.
Fourth, the teaching/T.A. experience will have almost no bearing on your application. The conference presentations in an altogether unrelated field may help a little at the margins, but unless the adcoms have familiarity with the relative prestige of those conferences it will not help much either. Similarly your research work may be interesting, but adcoms will be unfamiliar with your field and the quality of your research.
You probably have a better chance at one of the Data Science/Analytics PhD programs you mention only because those programs are very new and are taking students from a wide range of backgrounds, so long as they have sufficient quantitative and programming skills. Some of those are based out of B-schools, but some are not (NYU's is run out of an interdisciplinary Center for Data Science).
If you really want a B-school PhD, and you want a field where your petroleum engineering background is more likely to be recognized and appreciated in the application process, you might have a better shot at programs in Operations Research or Operations Management or Supply Chain Management. (Perhaps this is what you meant by "Management" but in B-schools when we talk about "Management" without prefacing it with "Operations" or "Supply Chain" it refers to the field known as "Management" which is roughly split into two subfields, Organizational Behavior and Strategy)