Getting a Green Card for a 6-12 Month Stay

Hi

I have questions regarding the green card. I entered the US on a J-1 visa that recently expired. I'm married to an US citizen and we are planning to move to my home country Germany in 6-12 months. That means that I don't really want to immigrate, I just wish to extend my stay by 6 or more months. Since I am late for changing my J visa to another one is the green card really the only option I have to remain in the country? I know that the green card is quite expensive and it takes such a long time to get it. And even if I would wait all that time they would probably cancel it as soon as they find out that I am not actually staying in the US. So all that money and work for nothing...
Is there anything else I can do besides applying for a green card? I overstayed on my visa for 1 month now, would they maybe turn a blind eye and change my status to a K-3 visa or something??

thank you so much for your help!

Instructions for applying for a K3 are here.

I'm not sure it would be granted, due to your overstay, however. It's in your best interests to consult an attorney.