Hi "Funnyface",
Maybe you are not aware of this, but there are 2 international schools in Tivat. The second one is called Arcadia. It could be worth sending them your CV too.
There are 2 ways of getting a residence permit here, the first one is if you have a job here (your work permit will entitle you to a residence permit) and the second one, which is new and will be in application from April 1st 2015, is by owning property in Montenegro.
Cheers, best of luck, and welcome!
Carine