One other interesting way to approach this issue is use LinkedIn to figure out where people who went to your undergrad school are now working. Find people who now work at the companies you want to intern in. Do the above (write them a nice email asking about their internship opportunities).
The key here is not to write 1-5 emails or to write 1000 to 5000 emails. The key here is to write about 10-20 emails that are hyper-specific to each company and each situation. What you are looking for is responses at this point, not internships.
Once you get a response, you can get started talking to the right people.
I graduated in from a research university in Czech republic, and met several PHD students from non-eu countries who were quite happy here :) If you cast the net wide enough you might find a place that suits you. Just be wary, that PHD programmes vary widely in quality, aviable stippends/grants, expectations of work input, or applicability for your next career.
I had friends part-timing PHD study while interning at a company via some partnership programme, with reasonable monthly income, e.t.c, and I have seen some other friends slaving away for 200Eur/month for 10+h/day at a lab.