I tried refinancing but have been declined several times even with good credit and clean mortgage payment history for 9 years. What if I put the property up for sale at the appraised value (not underwater) and buy it back? Sounds crazy, but that way, I can sign a new mortgage (perhaps with a new bank) for lower interest rate, get rid of the secondary mortgage, plus try for 15 year mortgage for an even lower rate. I'm sure the closing costs are minimal as there are no brokers involved or title searches needed. I'm sure I'm missing something here. This came to me during a drunken stupor.

If no lender will refinance, then no lender will write you a mortgage. Same thing!
Perhaps with a different bank? Why haven't you tried to refinance with a different lender? Do you think that 'refinance' means you have to apply only to your current one?
And closing costs have nothing to do with broker involvement.
Goodness, drunken stupor indeed.

You say you have been declined several times, have you been given a reason for the decline? If you have equity in the property with good credit I see no reason you should not get a refinance. Have you only applied to your current lender?

... I'm sure I'm missing something here. This came to me during a drunken stupor.

Yes, you are missing quite a few things.

For one: a title search (for the required title insurance) is always required.

Stop drinking and get your ducks in a row and explore more sober options. Why were you declined before? Lets start there.

What are you calling a "good credit score". Because that is key to everything.

I don't consider anything less than the high 700's as "good", if its over "800" I'm surprised they turned you down. If its in the 600 range or god forbit the 500 range (would be surprised if you could get a loan in that range).

THe numbers mean everything as to what rate you would qualify for as well....