If US exporters want to claim back the sales taxes they pay on their imports they should be talking to their governments not complaining about the EU. VAT is paid by consumers. EU consumers pay VAT exactly the same way when they buy domestic or imported goods.
The current system in the EU does not "punish" US exporters, it "punishes" EU consumers for consuming (in the same sense that income taxes "punish" you for earning income). The US tax system "punishes" you by imposing sales taxes on you that you can't claim back if you use the products as inputs to goods or services that you sell. The EU plays no role in this whatsoever.
The US has identical treatment to everyone else, including EU domestic businesses. It is crucial to understand this. US exporters do not pay VAT on their inputs, so they have nothing to claim back from the EU. It makes no sense to say they are disadvantaged.
Check out the distribution map on Wikipedia :
https://en.m.wikipedia.org/wiki/Value-added_tax
This discussion is a perfect example of everything that is going wrong in the world at the moment.