That still doesn't make any sense. Consider the federal case. Currently minimum wage is $7.25/hr or just above $15k/yr, whereas $20 minimum wage is like $40k/yr, or like $18.40 after federal tax (ignore FICA + states for now, they're beside my point).
You're complaining raising minimum wage to $20 is not the solution, but you want to raise it some, and make up for the rest with lowering taxes? So what mix are you imagining will give comparable results? Like say, raise minimum wage to, I dunno, maybe $10? In what world is lower taxes going to make up the $8.40 shortfall? Are your taxes going to be negative? Or are you suggesting you're comfortable raising minimum wage to $18.40 but the $20.00 is what you find overly excessive?
P.S. I wasn't even talking about EITC, but the standard deduction. Your first $18,650 of income as head of household are simply untaxed ($24,800 for couples)... period. That's exactly what you were proposing, and it's been already there, for a long time. In hourly terms that's $9/hr for heads of households ($12/hr for couples) of untaxed income. EITC is relatively obscure by comparison, so I'm confused why you would first think of that when replying... I'm guessing you might be confused about how standard deductions and tax brackets work? Or possibly unfamiliar with the US tax system?