Divorcing the pay for 'minimum-pay positions' from the revenues of businesses (and government) would keep it from affecting costs. In this revolutionary (but not radical) proposal money would be created as needed to provide the pay for people working in those positions. It could be set at any amount: the higher, the more positions would be captured by it (as it would be gradually raised from, say, $10/hr.; $400/wk. to prevent inflation). There are intrinsic safeguards against inflation throughout the paradigm.

Employers would compete for employees to fill those positions through general working conditions and negotiated (in-kind) benefits (such as insurance, education, transportation, housing, clothing, entertainment, etc.). The pay would be the same for everyone receiving it, but conditions in different labor markets (geographical and positional) would determine benefits.

if curious: "Two Possibilities within MMT" ('Modern Monetary Theory') here in Medium, but not behind the paywall