I have answered you before.
The K2 visa is for a child of the K1. So what they are telling you is a lie. You can't get a visitor visa and then file for the K1 or K2 here. K visas are only issued abroad through a consulate.
I believe you are being scammed again and it really distresses me to see you being taken advantage of once again by this "police officer".
Your true love is playing on your vulnerable state and going to put you into more debt than you can handle.
Please let this go!
You need to be concerned about not only your 180 days, but abandoning your resident status in the US.
At any time you go through inspection the officer can look at all the time you have spent out of the US and decide he thinks you have abandoned your ties to the US. You say you "have your life set up on London". That is a big concern.
If you can' show a US job, residence, financial ties, etc, they can set you up for removal proceedings as one who is only visiting the US and who has abandoned their residence here. It happens all the time. You are a prime candidate. You need to read this link and pay particular attention to Maintaining Status
So you are only focusing on one issue here and ignoring the bigger problem of totally loosing your resident status. Google "abandoning us resident status" and read what you can find on the subject. You can also put that into the USCIS home page search engine and read about it. http://www.uscis.gov/
What I am telling you here is you are walking a tightrope. You might skid by, but I'd not go beyond the 179 days and then spend more than a weekend in the US!