Well, we did decide to get married. Not for the permit actually, but that was kind of a bonus. However, as the rules are getting more lax (esp. for new-EU citizens), I bet this has all changed. But, just to give you an idea,
this is how we did it. And I was able to stay like 3 months extra before the wedding (on top of my 2x180 days). I have friends who got a sort of fiance visa without getting married. The guy (HUN-CH citizen) signed a paper saying he'll support her, she kept her Hungarian insurance, etc. and she got a one-year non-working B. But she found a job within the year and got her permit updated without much hassle. Might be worth a try.