I had the same questions as John on this.
As for the USDA vs FHA scenario, while the USDA has lower monthly insurance costs, the qualifying ratio for a USDA loan is much lower than a FHA loan (when compared to automated approvals). USDA wants to see your housing obligation no higher than 31% of your gross income, which on $5600/mo, would be $1,736/mo, you clearly wouldn't qualify in this scenario for the USDA loan.
FHA on the other hand wants to see the same ratios (the general guideline or manual underwrite) but the automated underwriting engine is MUCH more lenient on it's automated approvals. I've had clients be approved with as high as a 55% debt ratio (mortgage, insurance, taxes plus other monthly debts that report on their credit report) which would be $3,088/mo.
Since we don't know what your credit score is or what your reserves look like (cash reserves greatly influence automated underwriting's ability to approve higher ratio loans), it's impossible to give a yes/no answer without putting it through the automated underwriting system.
Feel free to call me if you'd like to run it through or direct your lender to do this for you as they should be able to tell you this without much trouble.