"Have you or somebody you know successfully made the transition from (non-computer) science into a tech career? In the current economy, what are the chances you'd hire a highly motivated science dropout with programming competence and basic stats knowledge?"
I did it, have worked with others who have done it, and would now hire people who did. The important part is your ability to program. There are tons of PhD students (even in CS), who can't (or won't) write code. There are even more who write horrible, unmaintainable code. You have to be better than those folks.
Also, do not be deceived by "data science": it's mostly a bullshit term, and translates roughly to "programmer who knows basic statistics", rather than "scientist who knows some programming". Nobody wants to hire you if you can't implement your theories in a production context.
The bottom line is that if you're a good coder, nobody cares how you wasted your youth.