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Your only option is a Conventional. Both Fannie and Fredde offer better options for consumers with student loans. We are allowed to use your IBR not the 1% like FHA or USDA. Let me know if you have any further questions.
Best wishes to you
I just went through / am going through this issue. The bottom line is that no lender I know of (Conventional) will accept a $0 payment. I recently consolidated my student loans and Fedloan (seriously the worst) reported the consolidation and a $0 monthly payment!!! I'm on REPAYE. The reported this on Feb 31, 2018 and hadn't updated since then to the actual payment. Navy Fed accepted my IDR paperwork showing my monthly payment without any problems. They refused to take the $0 payment listed on my credit report (which was clearly incorrect).
Bottom line - try to get at least a $1 monthly payment on a new IDR program. As soon as it gets approved, get all the paperwork, and then dispute your credit report to have it updated to the new monthly payment. You should be good to go, but only with a conventional mortgage.
I would recommend you search for small banks/credit unions in your area that specialize in low down payment conventional loans that can take the IBR into consideration. What if your significant other were to carry the mortgage alone instead? Is that an option? That is what my partner and I had to do due to my high student loans causing my DTI to be outrageous.
If you get a letter from FedLoan stating your actual payment, the Loan Officer can correct the report. I've done it dozens of times.