As a member of your LLC, you should be able to sign any documents without a POA. At least that's my experience. I don't know why a POA has been requested. Perhaps I don't understand the way real estate transactions work in Cali.
How far along are you in the transaction? Do you have a ratified (executed) contract? Is this a cash deal? Being that your LLC is newly formed and has no established credit, any mortgage will likely have to be taken out in your own name. Maybe this has something to do with bridging the gap between you as an LLC member and you as a mortgagee.
Articles of Organization are completely different than a P.O.A. I'm not sure what an "escrow officer" is. In MD we use title attorneys to facilitate the transaction between buyers and sellers. Title attorneys can draft POAs, which are fairly commonplace in real estate transactions (when one party needs another to sign on their behalf.)
"The first lesson of economics is scarcity: there is never enough of anything to fully satisfy all those who want it. The first lesson of politics is to disregard the first lesson of economics." Thomas Sowell