Correct - conjugal won't fly if he's from NZ. You face no barriers to marriage or common law.
You really have two choices: (1) get married; (2) find a way to live together continuously for a minimum of one full year. The second option may mean that he comes to Canada as a visitor for six months and then extends his stay from within Canada for another six months so that you can apply once a year has passed. Since he's here as a visitor, he won't be able to work. No - this isn't the same thing as applying inland. First of all, you should apply outland. Secondly, you won't be able to submit either an inland or outland application until you are either married or common law.