First of all let me be on record as saying if you are negative live with your current car little while longer until you are not negative. Ok off the soap box.
Most banks, CU, capital1 blank check, etc, allow loans up to 100% of MSRP of the car. This is to cover things like tax, title, tags, processing fee, etc.
Now since you are a good car shopper and will go to edmunds.com to find invoice and not pay more than $500 over invoice and subtract any rebates from price it is possible your car may be $3K, $4K, $5K, etc less than the max the bank allows. You don't need to be financed through the dealership.
Most CU and Capital1, USAA, and couple other lenders have "blank check" programs. You get approved for a max amount say $30K. Then you write check for amount of the sale. The dealer just needs to be sure it is no more than 110% of MSPR. Of course since you are smart shopper and will use edmunds.com, find out what rebates are available, try multiple dealerships and not accept any offer than is more than INVOICE - REBATES + $500 this won't be a problem (hint, hint).