So much for the Streamtech internship idea -- I just got an email from their CEO in response to my application. "I'm afraid we have very recently had to conclude that, mainly because of immigration laws, taking on interns from outside the EU is no longer feasible for us. Unfortunately, you have caught us right between concluding this and updating the vacancy descriptions everywhere. My apologies for your wasted effort."
I don't know very much about immigration law, but I imagine that if they're affected, plenty of other companies are, too. That's really a shame for anyone in the rest of the world who might have wanted to work in Europe.
Luckily, I don't think my effort was the least bit wasted, since, funnily enough, writing code appears to be a good way to get better at writing code and applying for jobs appears to be a good way to get better at applying for jobs. (Speaking of which, my Google phone interview is on Friday!)