Single Member LLC pays mortgage, but the title and mortgage is under my name.

So I own my own LLC, and it is a single member LLC. I was originally planning on putting the property under my LLC until I learned I had a due on sale clause, and could not put the title or mortgage under the LLC. I already have the property setup through airbnb and VRBO and it is being rented, all income is going to the LLC, and the LLC is making the mortgage payments, and all expenses are paid by the LLC (which uses a business bank account). Is it advised I try to refinance and get the property under the LLC? Can I keep this the way it is?

I know that with this setup I do not have the liability protection which I can live with for a little bit, but if this complicates taxes and everything then I definitely dont want to make my life harder and I would like to learn what the best thing to do here is. I also want to mention too that the LLC does not pay me personally, I do not take money out. 

What should I do in this scenario. Keep it so the LLC does everything except it doesn't own the title, and if so, would I file taxes as a business, or would the mortgage and interest taxes go under my personal, I have no clue what I am doing at this point so all and every piece of advice is welcomed.