The lever that moves fastest is the appraiser's market rent estimate, because self-sufficiency runs off the appraiser's number for all four units, not the rent roll. In-place leases at $1,250 don't cap it. If your own comps support $1,375, that's $5,500 gross, $4,125 at 75 percent, and you clear $3,900 with room. Pull three or four rented two-bedroom comps in the same submarket and give them to the lender to pass along, since appraisers can accept data they didn't find themselves and often do.
The second lever is the payment. More money down cuts principal and interest, and it also cuts the annual MIP because that's charged on the balance, so a move from 3.5 percent to 10 percent down does real work on both sides of the test. Price reduction does the same thing and costs you nothing, and a fourplex that can't pass FHA self-sufficiency has a shrunken buyer pool, which is an argument you can make in writing.
The third is a different loan. Conventional owner-occupied financing on two-to-four units has no self-sufficiency test, and low down payment options for owner-occupied multifamily exist on the agency side. Confirm the current down payment minimum and reserve requirement in writing with your lender, because these change and pricing on a 2-4 unit investment-adjacent product is not the same as a single family quote.
What I'd worry about more than the $150 is the FHA appraisal itself. An FHA appraiser on a dated fourplex writes repair conditions, and a seller who won't fix peeling paint or a bad handrail before closing turns your financing into a stalemate. At 3.5 percent down, the annual MIP also stays on the loan for its full term, so a refinance later is the only exit from it. Price that into the hold, not just into month one.