FWIW I am in the same boat, and have been for a few years since this global shipping thing started. Typically the seller offers no other method of international shipping, which for them is a reasonable scenario. Quite what happens to the VAT is beyond me.
I’ve heard the argument that it’s for personal sales only, but every other international shipper seems to be able to deal with it.
Don’t misunderstand me, the treatment of VAT and its collection varies hugely between states, so it’s not trivial to set it up correctly.
On a side note, the quality of the shipping logistics itself stinks, you item takes a long time to arrive by modern logistics standards, and seemingly your items sit in Erlanger Kentucky for days on end. On one occasion I’ve had a shipment returned to sender before it even got out of the US, and on another occasion I received the wrong item after it was re-packed by Shitney-Bowes, one of the “services” they offer sellers.
It’s a badly thought out, and half baked service.
So I’m sorry, in short, I don’t have a solution for reclaiming the VAT.