Would a 15% across the board import tax get us some way to a national sales tax? Seems so, but with, as you point out, serious and undesirable side-effects.
Personally, I think a 15% or so VAT is what we need, but that's not going to happen.

That does raise another small problem with taxing imports: there just aren't enough of them.

At a guess, 6% VAT would probably be enough to wipe out the problems of the federal deficit. Maybe even as low as 4%: there is no problem with a deficit over the long run, even with forever rising real debt, as long as the debt doesn't rise faster than real GDP over time. According to figures provided by an LLM (i.e., might be wrong), the US trailing four quarter deficit was about $1.3tn and final sales of goods and services to individuals were about $21 trillion, so about 6%.

But imports are only maybe 10-15% of that, so to raise the same revenue as a 4% across-the-board VAT (which wouldn't wipe out any businesses) would be maybe 25-30% across-the-board tariff (which would break whole swaths of the economy).

My cockamamie solution: National VAT with no exemptions, plus a fixed tax credit per household of maybe $1200 so nobody in the bottom quintile ends up paying more. Then just pass a law that the federal VAT rate is whatever would bring the deficit under (say) 2.5% of GDP, averaged over a few years. Lawmakers that don't like the idea of a national VAT are not thrown overboard: they need only move a little more towards a balanced budget in other ways at any time, and the rate stays at zero!

Jim