"you state you have perfect rental history and almost 12 months of car payment" this paints a picture of what might span 36 months or so...which is 1/10 the amount of time you will have a home. Because of this your credit score becomes valueable because it spans 10+ years, or at least 5+years, and if it is Low, it may very well be because you have not had it long. you need to work on improving your credit that will be your best solution, which should only take 6-12 months...
Try getting a NACA mortgage. Have you Realtor sign you up so she can represent you. If you go to the NACA website yourself you will be required to work with a Realtor they chose so contact your Realtor today and tell her you want to get the NACA mortgage.
Here's the website, but remember DO NOT sign up until you have chosen your Realtor and she logs you in:
If you don't have a Realtor yet, contact me and I can give you a great recommendation in Ponte Vedra.s