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#1, how are you determining this new home has $100k in equity? If you are paying X price, isn't that what the home is worth? Looking at sales prices no more than 30 days ago (since you are in Miami) would be what you would want to base your estimate on how much equity this home might have after you purchase it. Also keep in mind that you are buying this particular home for a particular price, what happens when the same model home gets sold 1-2 months from now for less than what you paid? You now have negative equity. So if you are buying the home is based on the perceived amount of equity, make sure you aren't using outdated info to make that assumption on.
#2, refinancing and quit claiming your home to someone else isn't going to remove that mortgage payment from your debt to income ratio, you would still have the mortgage in your name. Since you don't have the required amount of equity needed in order to consider rental income from your current primary residence, the only way to remove that from your debt to income ratio is to sell the home.
#3, it usually takes 1-4 weeks to hear back from a foreclosure in markets that are experiencing high foreclosure rates, and with the holidays and all I'm sure it has added some time to their response times.
#4, if you exclude your current mortgage out of your income calculation, and would only have the $426/mo car payment, then your debt to income ratio looks fine to buy the new home.
#5, what does your loan officer say about all of this?