Well depending on how low your credit is will determine if trading is a good option. You can not sell it unless you have all the money to pay it off and get the title with the lien released.
You could take out a home equity loan if you have enough equity and pay the car off. Then sell the car and pay off the amount you receive for the car on the home equity loan. Then that would leave you a small balance on the equity loan and you could pay that off quickly. Also the interest on the equity loan would be tax deductible.
Then there is the option of trading it, you will be further upside down then the $3400 if you sold it on your own because the dealer is only going to
give you trade value for it maybe a bit more. Find a car with a good rebate that you can buy as close to invoice as possible and this will help eat some of your negative equity and with starting a new loan term could lower your payment. This will cause negative equity in your new vehicle though.
My main concern here would be loan options because if you make $250K a year that is $20,833 a month give or take a few dollars. Then your house payment is $2400 and your 5 car payments are probably a few thousand and then I am sure there is some credit cards, other loans etc. so you need to make sure your debt to income is in line or that could throw a few kinks in a loan whether it is equity or trade.