Interns in other industry pay for an education with time and effort I know of none where they are asked to pay to work.....
Historically the best route into a career in aircraft design is probably the Cranfield MSc, which still runs, and is still arguably the best in the world: I've been invited to their end of course presentations the last few years, and am consistently extremely impressed.
It'll cost you £10-£20k for a year (plus your living expenses), and you'll spend several months of that working at your own expense on somebody else's design or research project ! The good news is that those people then tend to go into extremely good jobs very quickly - whilst there's a surplus of job-hunting fATPLs, there's a shortage of good MEng or MSc qualified engineers. If anybody's tempted - link below...
https://www.cranfield.ac.uk/courses/...le-design.html
That said, I'd struggle also to think of any professional education quite as expensive as training as a professional pilot - and pay-to-fly is particularly dubious.
G