Here is the real red flag for me, even more so than the ‘need imporovement’ credit (685) or the low down:
You dont live here yet, and own a house somewhere else?

This should have been disclosed in the OP, because it is a huge fact to me. San Diego is a VERY diverse city, and I would advise ANYONE moving here for the first time to rent. I dont care if you are Bill Freakin Gates, RENT YOUR FIRST HOUSE. You will not know where you want to be, and what kind of lifestyle you want/can afford until you are here. The housing, the noise, the weather, the people, the social scene, the activites, they are all so different.

Find what you want, then optimize it to what you can afford, and live the happy median. SD housing prices are stagnant or falling currently, interest rates are low, and going down. Rents are not skyrocketing. There is no possible reason you NEED to buy a house, in a city you dont currently live in, in the next 6-12 months. (unless someone else is paying the tab for you, which again is a fact needed in the OP)