You need to interview several lenders to see what products or loan packages are available. Lenders vary in types of loan packages and interest rates. I am working on two VA home mortgages right now with different lenders, different loan products and differen interest rates and both required a minimum 640 credit score. Personal debt is also a big factor as with any loan.
It is possible with that fico score to get VA financing, however I suggest to simply apply online for a more concrete look at the scenario. You can easily go to http://www.wichitahomeloans.com and use the apply now feature. Only takes a few moments, and we can get you on the proper path!
If you are shopping for a loan, don't have a lot of mortgage companies pull your credit. Each pull will drop your score. Stay away from on line lenders, like Lending Tree, where they "Compete for your business". Each lender on lending tree will pull your credit, dropping your score several points.
You need to work with a lender, locally, who is willing to help you raise your score, by guiding you through what will improve your score to 640 or better. Do not do it yourself, without guidance, you could make it worse without meaning to lower your score. Lending is always the first place to start when looking for a home. I can recommend lenders who do VA and will help you with your score.
Please let me know if you need assistance finding the right home once you become pre qualified. I am a licenced real estate agent, here in Wichita and I'm also a veteran from the Marines. I would love to work with you to find a home!
Second; is that 620 the high score or the middle score?
It sounds like you have already tried.
Some lenders may go your bond, if your DTI is low enough. It would be up to the Lender.
Keep trying to raise that score.