I'd suggest figuring out which niche of data science most aligns with your personal interests and start there. Hiring managers don't discriminate based on "too many years in academia", it's more what's the reason they should hire YOU over candidate y?
Diehard animal lover? I bet the Sierra Club would love a statistician who could help them quantify how many elephants are being poached in Africa per year.
Interested in sports? Strava gets millions of data points a day, I'm sure they're looking for help finding signals in the noise.
Can't get enough of financial markets? Finance jobs all over the place for quants.
If your profile is too generic they'll see no good reason to hire you, but if you're passionate about X it can really work in your favor.
The job search is depressing but never give up hope.
But that brings me back to my original point, you have to find a place where your personality and interests are a match, not just RandomJob.com.
If you have a higher degree in math, there is always another job out there waiting for you.
Typical interview for higher jobs aren't focused on tests or quizzes. If that's what your getting your not applying to the right places - and there might not be many places.
It could be true in some fields (biotech and life sciences, pharma/chemistry, "real" engineering, ...) but in math/CS?
Most companies hire PhD grads at one job grade/level above entry-level, i.e. it's typically not worth much more than a ~2 years head start salary-wise. If a candidate has spent 4/5 years gaining experience in the specific skill set you're hiring for, that's a bargain.