Transferring a deed into an LLC, but mortgage is not re-assignable?

[Bob Jovins]

Hello all, glad to be here. My wife and I recently moved, and we want to rent out our previous residence. It's a single family house in NY. The deed is in my name and my wife's maiden name (we purchased the house before we got married). The mortgage is also in our names. We want to transfer this property into an LLC for liability protection before we rent it, but the mortgage is not re-assignable.

I was hoping we could continue to pay the mortgage either personally or from the LLC and hope that the bank didn't mind, but that carries the risk of them freaking out and calling the mortgage. My attorney recommended attempting to refinance the mortgage, which would essentially create a new note that we could assign to the LLC along with the deed.

I'm not positive we can qualify for a refinance currently, but we'll try.  That aside, does anyone have ideas for what the best way to handle this is?