Ask HN: How to avoid being typecast as an engineer?

Hi HN, I'm currently in an employment dilemma where I want to move into an ML engineer or Data Scientist role at another company, but I've spent the last 3 years as a Data Engineer and other companies seem only to want to hire me for that. Previously I've worked on web and mobile development.

I've tried joining a very early startup to gain the social capital to work on data analysis and machine learning, but our company seems to be going in a different direction (just moving data from A to B for people). I spend a lot of my free time studying machine learning and statistics (and writing code for it); right now I'm strongly considering going back to school for an MS in Data Science.

Any advice for "reinventing" yourself in industry? Employers seem to be concerned with immediate usefulness, not long-term training of staff and flexibility in worker roles.