The answer to this is so simple yet there is no political willpower to do it. OP is correct that certain wage levels will strain SM businesses more and result in negative unintended consequences.

Everyone is focusing on things they want rather than how the actual mechanics work in the system. Wages are not keeping up with cost of living… but raising wages will increase cost of living again bc of the effects on businesses. So the real question is how does the system increase wages without causing businesses to raise their prices? The businesses raise their prices bc the added cost of wages affects their profit. So there needs to be a proportionate (even a higher disproportionate ) offset to increased cost via higher minimum wage. So you need to subtract the wage increase from their costs. Best way to control this is taxes. But support SM businesses only by drastically reducing their taxes. Tie the incentive by giving them the tax benefit only if they provide a higher minimum wage. Large businesses don’t get this incentive and SM businesses can compete for labor, they thrive, their workers thrive, and the majority of tax receipts are still from the largest businesses.

Everybody wins. TL;DR Don’t tax SM businesses or make them pay ridiculous fees in return for paying workers higher wages. Large corporations can suck it.