In no particular order, I will begin by the issue of the visa. You have to realize that european universities accept students from all over the world. This is why visa students come with restrictions and should be avoided as much as possible. Working visas are the only thing that matters from a legal immigration viewpoint.

Second, you also have to realize that european universities produce far more graduates on humanist sciences such as languages, philosophy, psychology, history and so on, than the job market can take. At the same time the situation is almost at the opposite about anything around engineering. One could argue that Europeans become a people of epicurean philosophers with no one to repair the electrical installation :)

Third, while your situation is not a matter of integration, you must also realize that that problem is posed when immigrants are already in. The wave of xenophoby you might feel in Europe is mainly related to three aspects:
illegal immigration (mainly from northern Africa into Italy, Spain, or Greece; also from Asia into the UK or Scandinavia);
work immigration concerning the latest EU members from the Eastern Europe;
and immigrants already in possession of their permanent residence or even citizenship, and not being integrated (for various reasons, imputable to both sides); this is particularly feeding xenophobic feelings: locals have a hard time calling this people "French" or "German"; they have a hard time describing themselves as such anyway.

The fact that you're so wonderfully integrated matters a lot, but not when there are legal problems. Bureaucracy always swears by the law, even if your obvious integration (and your white skin, because prejudices are a human quality) puts them in a friendly disposition.
I can assure you that an indian or algerian in possession of all required documents is treated absolutely professionally, and at least in France he'll have a good chance of talking to a clerk of his own race, since they started to staff immigration offices with people of foreign origins. He won't have a problem with xenophobic feelings, let alone policies; that may happen afterwards, if he doesn't integrate successfully.

Finally, all western countries protect 1) their job market and 2) their social security systems. It's a problem of money, and nothing else. If they don't need astronauts, they won't give them visa, period. There is no way to go beyond this. They welcome doctors, nurses, or engineers, because these are the profiles in low supply. Immigration is easier in NZ, Australia or Canada because those have always been immigration countries and have the required infrastructure as well as the necessary culture, but even them sort out candidates by their work field.
In short, the best way for you is indeed to find work as a teacher and then get a proper work visa. This is where your integration will help. Then you'll be able to find out if and how you can profit from the years you already spent there as a teacher, in view of permanent residence.

Hoping this will help,

Free at last! Free at last! Thank God Almighty, we are free at last! (Martin Luther King)