German universities are always hiring. Always. And in my experience they need just about everyone

If you have an Irish grandparent you can get a passport. Lots of work here and Americans are welcome.

Otherwise work visas that turn into residency aren't difficult to come by with sponsorship and it's not the kind of sponsorship that makes you a slave.

In my faculty, there's often vacants for lab technicians, if you want to give it a go

The pharma industry is currently booming in Denmark (Novo and others are expanding like crazy), so perhaps you could try and look into that