My contractor called the payoff figure a "soft number" and I still don't know what that means

Your contractor was right, and the mechanism is exactly what you described. Borrowers quote principal because that is the number they see on their last statement. By the time a servicer issues a formal payoff demand after a notice of default, that figure has absorbed accrued interest to the payoff date, late charges that have been compounding since the first missed payment, any forced-placed insurance the servicer added, and attorney or trustee fees that started accruing the day the file went to foreclosure counsel. In judicial states especially, those legal costs can run high because the process is longer and the servicer's attorneys bill hourly.

The assumption doing the most work in your original deal was treating the seller's number as a ceiling rather than a floor. It is almost always a floor.

On a stress-test rule of thumb: the gap between a borrower's stated balance and the formal payoff demand depends most heavily on how many payments they have missed and whether the servicer has engaged counsel. Two payments missed with no attorney involvement, the gap might be a few hundred dollars. Six or more payments missed in a state where the servicer uses outside foreclosure counsel, the gap can run $8,000 to $15,000 or more before you factor in any escrow shortage. Your $11,400 shortfall on a delinquent loan is well within normal range for a file that had already progressed far enough to have an auction date.

A working approach: ask the seller directly how many payments they have missed, then build in a buffer above their stated balance based on that count. Some operators use a flat percentage, something in the range of 8 to 12 percent above whatever the seller says, as a provisional floor. Confirm the actual figure with the servicer's loss mitigation department as early in your window as possible; some servicers will give you a preliminary verbal figure before the written demand if you identify yourself as a potential purchaser. That call costs you a day, and you had 34 days, so the math favors making it early.

The risk you did not name is timeline compression. Every day you waited for the demand letter was a day not used to renegotiate, line up a replacement buyer, or kill the deal cleanly. With 34 days to auction, day six is already late to learn the payoff is wrong.

What state was this in, and had the servicer already referred the file to outside counsel before you got the demand letter?