It all depends on what FHA's automated approval software says about your application. With substantial reserves (FHA requires you have at least $100 left over after closing) it may be possible to obtain an automated approval from FHA Totalscorecard. With an "Approve/Eligible" rating, you'd have a range of lenders to choose from. Some lenders might cap your debt ratio at 43% regardless of AUS (Automated Underwriting System) results, but I can think of 5 lenders right off the top of my head that will accept debt ratios over 50% with an "Approve/Eligible" from FHA Totalscorecard.
The problem with working with banks or direct lenders, in your case, is that you'll have to "shop" them one at a time... a very lengthy process. A mortgage broker could contact dozens of possible lenders in an afternoon to determine if you meet their guidelines. It all depends on how much time you want to spend on hunting around for a loan.
If FHA Totalscorecard comes back with "Refer/Eligible", you would have to work on the debt ratio to bring it down to 43% or less (to meet manual underwrite guidelines). Lenders vary widely on how to restructure your debt... again if you work with a bank or direct lender like Countrywide (now part of Bank of America), you would have to shop lender after lender until you found one that has the right combination of guidelines, investor tolerance of compensating factors, and of course pricing and rate. A mortgage broker could help you with various debt restructuring scenarios (pay down credit card debt, increase down payment, etc) to match the best lender guidelines.
By the way I've been a mortgage banker, mortgage lender, and run a mortgage brokerage. All have their advantages and disadvantages. In your case, it would seem that a broker might be able to speed the shopping process.