Please update your timelines. Most likely eac card received before advance parole. You can apply for parole but probably waste of money as green card will be received before.
What kind of entry did your significant other come on.? If that's the intent to marry before you entered and adjust status that is not recommended. USCIS will think you're jumping the line.
I don't think your plans will work. K1 is for marriage within 90-day arrival. Either consular process or marry and file i130 and 485 together along with I864 I765 and 693.