Not sure where you live, but for the bank I work for, PNC Bank, we do home equity loans, first liens up to 89.9% financing, up to 30 yr terms, with avg closing cost of ~$200 in PA. Appraisal is paid for by the bank.
Another option, thru PNC Mortgage is an 80/10/10. 80% Mortgage, 10% home equity piggy back, and 10% downpayment. This allows 10% down and no PMI. - PNC Mortgage does business in all 50 states.
Firstly, I believe Zillow is good for a rough idea, but they have no idea what the inside of your home looks like, I would say try your local bank to see if you can apply for a home equity, they'll often eat the appraisal price.