I have a German friend, who has been living in the US for a couple years
She has insurance from Germany with Hanse Merkur
They have a policy covering various other countries (you'll have to inquire if applicable in your case)
You can only sign up with them, while still in Germany before you leave, there's certain number of day requirement
Coverage can be taken for as little as two weeks, or a max of several years.
She's had to see doctors here in the US and is quite happy with her coverage
I can try and find out more if you like, or you can just go on the Hanse Merkur website and see what policies they have
I have had long term travel policies, while living in China, I need to see, which company I used and which countries they cover,
but I'll have to go dig a bit, as that has been years ago!