Sounds like you know your options (pay the new larger payment of new escrow+mortgage+shortage or come up with the $7700 shortage and pay the somewhat smaller new escrow+mortgage payment monthly).

If it were me, I wouldn't take out an interest bearing loan to pay off the shortage when they'll amortize the amount over the next 12 months interest free, unless you don't have the cashflow to cover that monthly payment. If that's the case, I'm not so sure you can comfortably afford to take out a personal loan to cover it, either. What does your total budget look like? Maybe the new car is the larger issue here? Also, is this a new construction, or have you otherwise verified that the $7700 shortage is accurate?