Learn R and machine learning (this will take a while). Move to a major city. One of the biggest career benefits you have as a scientist is experience with real data. If you can't get a job in the sciences, get a data science job. You are very qualified for a better job than most companies will give you at the entry-level with a hard-science BS.
This is a perilous route. Learning R and "machine learning" (probably meant as a catch-all for graphs, statistics, machine learning, and a dash of distributed systems) is necessary but not sufficient, since you'll be competing against people who know all of these things and have significant research experience, given the oversupply of PhDs in various hard sciences (the Python astrophysics community is booming, for example--they'd be immediate "data science" hires).
The net result is that you might end up in a BD-type analyst role, which may not be bad depending on your goals. It wouldn't really hit the engineering target, though.
Hah, yes. I don't know if the comment before yours was intended to be advice to me, but I'm one of those python astrophysics people (professionally). I deal much more on the data and distributed systems side much more than the analysis side, or really... I write software and frameworks that the analysis guys (from several very large experiments) use.
I think it depends on the company. There are a lot of terrible companies that won't look at you for an ML/data science role without a PhD. That's true. There are others that will hire smart people and give them a chance.
What will probably happen is that the pool of "data science" jobs will grow, but the bottom half won't be real DS.
I don't mean to imply that a person can become a decent data scientist overnight. It takes years, but it can be done.
On Wall Street this sort of role is called a "quant", although there's less machine learning in finance than one would expect (hard to audit). "Data scientist" is a startup quant. Just as with quant jobs, some firms will only hire PhDs with research experience, while others will take chances on smart people without it.
There are a lot of terrible companies that won't look at you for an ML/data science role without a PhD.
I'm arguing that it's more serious than this: there are so many PhDs out there right now, companies will have no lack of skilled, well-credentialed candidates to choose from. Going down the "do it yourself" DS route is thus (a) very difficult, and (b) not very likely to pay off.