How can you move to a country that only allows for short term visits?

You can't do things it that way or you will encounter problems for sure ...

Staying illegally on a foreign soil isn't recommended. You must go to their embassy, and ask for a work permit / occupation permit / visa (the name is not always the same). Or you can spend one week or two in the country and ask the local administrations.

It is more complicated, but it's the right way to do it.

Thank you, Julien....
That is the way I had (prior to the idea I wrote of) thought would be a good way to go. I've got a U.S. passport, and original thinking had been to go to Canada, since my father was born there & was a Canadian Citizen at the time of my birth.  Thought I'd go there like as a visitor - no Visa necessary from here to there for up to 6 months, then apply for my own citizenship while there. I wrote to the Consulate, as I couln't find conclusive info on their official website, and got back a response that I can't do that. That I must apply for my own citizenship from the country where I was born, can't do it from within.  Hence, I got thinking of another way... I forget which part of this forum I read a particular post, but someone from the US wrote something to the effect of that it was urgent to get out of here quickly, as he thought he would be trapped here if he stayed much longer. That is very much the way I've been feeling for a while, and now even more and more so.

But I just read your reply - thank you btw - and you make it sound as if perhaps it IS in other countries O.K. to apply from within for *I know what you mean about things being called different things in different places* .... whatever it's called to be able to stay there, rather than here...