You've already pointed out a lot of the pros and cons...but here is how I'd summarize, and then I provide some specific advice below.
Pros: GMAT (if you get it 700+ as anticipated, given you're at 690 in bad conditions I think you'll get there), solid undergrad GPA, accounting work experience, CPA
Cons: Quantitative prep and research experience
Suggestions for quant and research:
Quantitative prep: I certainly wouldn't pay $1,200 for an online course. I think coursera and such is viewed just fine for showing that you are committed to improving your quant skills. If you want something more structured/formal maybe look at your local community college. I'd think you can find a formal course for far less than $1,200 is that's the route you are wanting to go. Also, try to think about other courses in college that could also signal your quantitative ability. Did you take something like a calc based physics class or something that can also help highlight that you can manage quantitative rigor?
Research: This is the biggest perceived (from the applicants perspective) weakness in most folk's applications. The vast vast majority of PhD in accounting applicants have zero meaningful exposure to accounting research. So you aren't all that far behind the eight ball here. You say you studied at a flagship university with a solid PhD program. Not sure if you still live around your alma mater, but I would recommend reaching out to some of the professors you had there and see if any of them would be willing to sit down for coffee or something to talk about doing a PhD. If you aren't geographically close, then see if someone would maybe be willing to talk on the phone. This will get you back into their minds (which will help your recommendation letters) and could also potentially get you an "in" for getting some research exposure. Again, if you still live in the area of your alma mater, maybe you can start attending some of their research workshops. Also, start digging around in the top journals (JAE, JAR, TAR as top 3s...then also CAR, RAST, AOS, plus JATA and NTJ if interested in tax). You aren't expected to fully comprehend what all of these papers are doing, but reading some introductions will help to start formulate some more concrete research interests.
Where to apply: Cornell doesn't fit with what you've said so far. If you wanted to do behavioral/experimental work, Cornell would be your place. But if you're thinking archival and maybe analytical, then Cornell is not a good fit. Likewise, Cornell is not a good fit for tax. Indiana and Illinois have good folks in pretty much all areas and methods, their faculties are huge. Pitt is more well-known for experimental work. Penn State is primarily financial archival. Rochester is almost exclusively financial archival. Ohio State is mostly financial archival.