The VA also uses residual income analysis for determining "capacity". From the VA website:

The primary method of evaluating a veteran's income is the residual income method. Under this method, the underwriter determines that a veteran has sufficient income to cover day-to-day living expenses after paying housing expenses, taxes, and other debts such as car payments and credit card payments.

For example, if an 0-2 (with three years service) were receiving a base pay of $3484, a BAH of $2000 and BAS of $300, her total monthly income would be $5784. We would deduct her taxes (on the base pay), of about $800. She's single, without dependents so there are no childcare expenses. This gives her contributory income of $5084. If she had $1200 in monthly expenses (credit cards, car loans, etc), her contributory income is reduced to $3884. The VA requires a residual income of $491. In order to "trump" the debt-to-income ratio analysis, we would need residual income of 120% of that, or about $600; this would allow for a maximum housing expense of $3,200.

Using the "eight dollars per thousand" estimate, Lt (jg) Smith would be approved for a $400,000 VA home loan.

You should have no problem going over the 41% back-end ratio. You might want to try working with a mortgage broker who has access to many different wholesale lenders. The only reason you wouldn't be able to go over 41% is if you loan would have to be "manually underwritten". And that is only the case if your credit score is very low.