Your arithmetic is why most people's stated Plan B isn't one. Work the DSCR test the way the lender will. At $2,740 in principal and interest plus roughly $450 a month of taxes and insurance, you're at about $3,190 in debt service against $2,450 of rent, which is a ratio near 0.77. Most DSCR programs want 1.10 or better, so you don't get $364k. You get whatever loan amount services at 1.10, which on those rents is closer to $290k, and now the gap to a $412k payoff is $120k rather than $48k. The refinance isn't a contingency here at any leverage you'd want.
That leaves cash, a sale, or negotiating with the servicer. A call usually arrives as a demand with a short window, often around 30 days, and a retail sale of a tenanted house takes longer than that in most markets, so a sale-based plan means you're asking for an extension while you list. Sometimes the servicer grants it in exchange for payoff certainty. Sometimes acceleration moves straight toward foreclosure, and the timeline for that varies a lot by state.
The piece your numbers skip is the seller's $30k. If that carryback gets recorded as a second, it has to be paid or subordinated in any refinance, and a subordination request goes to a person whose credit report still carries the first. You also need her cooperation to order a payoff statement, because the servicer will talk to the borrower of record. Get an authorization to release information signed at closing and keep the original.
So the position you're actually taking is that the rate spread is worth carrying an unfunded balloon risk. That's a defensible bet if you size reserves against it and price the equity accordingly. It isn't a hedged one.
