An LLC is a business....I file a form 1065 with mine. I am too high of an income to just claim a loss, but I can carry loss over and deduct it from the next year I have a positive income. I also get loans in the name of my LLC (that I personally guarantee). Talk to the bank and say that you want to transfer it for liability purposes and ask what the options are for lending to an LLC, I have better luck with small local banks for this.
My CPA said the easiest way to save money on your personal taxes is to start a business; because you are actually spending money on the business of owning a rental property, but right now you can't always claim the deductions whereas the business could. Talk to a CPA, I get a lot of this stuff confused, which is why I hired one.
It sounds like you bought this property as a buy and hold. Long term, you are going to pay much more in interest if you extend the loan term. So, as a long term investment, you need to weigh your total life cycle costs that are going to increase if you refinance vs. the short term "cashflow" gain right now. Extending the loan may bring more cashflow now, but at the price of a lower profit when you finally sell. You need to look at the total lifecycle costs (purchase price, rehab, upkeep, interest, taxes, insurance, etc.) when you are doing a long term hold.
Its really hard for me to believe that a property that does not cashflow at a 15 year loan term is a worthy investment to keep. Surely there are other properties in your area that will cashflow at a 15 year loan term and also appreciate? But I do recognize each area is different, so maybe not.