I have seen the name spelt in numerous ways in England - often on mail sent to me!
So I know about frustration:-)
I believe that there is a suggestion that the KEAST name came to England with German miners brought in to resolve problems with flooding in Cornish mines - but that is not something that I have followed up (I have quite enough to do trying to connect all of the KEAST clan).
As far as I am aware, none of the KEAST folk have tried the DNA route - I think that there is still a lot of debate around the validity of it.
One thought to bear in mind when looking at censuses was whether the enumerators could understand the accent/dialect being spoken and if not, did they put the state of residence as the place of birth in order to make life easier?
Or if they asked "where are you from?" rather than "where were you born?" - it is not the same question and might get a different answer when somebody has moved around a bit.