What is the most logical next event?

How to pay off student loans with a mortgage
Identify the types of mortgage loans available.
You can typically get a second mortgage (home equity loan), cash-out refinance loan, or a home equity line of credit (heloc). Each of these loans has benefits and drawbacks that you will want to discuss with your lender.
Before choosing your loan option, have your lender compare each option against the other two, and get a second opinion. Second mortgage: you borrow against the equity in your home and receive a lump sum.