Income-tax regressivity is fixed by exempting the first ~$25,000 or so of income. A consumption tax can be fixed the same way: Send every U.S. citizen a monthly prebate (e.g., ~$200 per person, a rough estimate) to offset sales taxes paid on essentials up to the poverty line. This makes the effective tax progressive for low earners while keeping it simple.
No, you're trying too hard. You exempt staples from sales tax, more broadly and generally than under current sales tax schemes.
For example, all unprepared food items are tax exempt, period. If you buy a rotisserie chicken or a prepared entree at the grocery store, maybe there's a tax, but not on uncooked chickens, etc. clothing, toiletries, and medical items are also tax exempt. Maybe clothes, up to a per-item limit, say, $100 per item with items under that amount tax-exempt, above that limit there's a tax applied.
You can't start mailing everyone a monthly check to reimburse estimated expenditures, that just insane and a recipe for fraud.
There are states without sales taxes, and states without income taxes, but every state has one or the other.