Learn English – Word for romantic partner you are living with but not married to

There's not really one that I'm aware of-- or one that at least, as you said, doesn't carry other strange connotations with it or isn't long/awkward/wordy.

Honestly, I would just recommend 'boyfriend' for everyday use. I know it sounds a little juvenile (I've been with my girlfriend for much less time than you and it already feels a little insufficient), but it's a quick, easy term that people will immediately understand, and it doesn't always have to apply to less serious couples.

You can use roommate, housemate, flatmate and similar terms to indicate that two unrelated people live together. None of these words imply any particular relationship (unlike cohabitation, which suggests that they have a sexual relationship or partnership).

Wikipedia notes a usage difference between American and UK English:

In the UK, the term “roommate” means a person living in the same bedroom, whereas in the United States and Canada, “roommate” and “housemate” are used interchangeably regardless whether a bedroom is shared. This article uses the term “roommate” in the US sense of a person one shares a residence with who is not a relative or significant other.

Thus, you can use housemate anywhere to indicate that two people simply live in the same house. In American English, you can also call them roommates.