"It's my understanding that SSTBs are specifically excluded from eligibility for the deduction."
You misunderstand SSTBs can get the199A deduction but the computation is more complicated than for non SSTBs if taxable income exceeds the threshold of taxable income of $340,100. the QBI computation is done on form 8995 if your taxable income is below $340,100 otherwise form 8995-A is used. By taxable income I mean the amount before the QBI deduction
example taxable income before QBI $300K
SSTB S-Corp QBI income $250K
taxpayer gets a QBI deduction of $50K
same as above except taxable income before QBI $350K
taxpayer gets a QBI deduction of $40.59K
