"within the EU you can presumably claim (VAT) back if it's a business-related expense as part of your tour"

Won't that apply only if the band or musician is VAT-registered?   A very large number won't be.

So far as I am aware an ordinary consumer can't recover VAT on services abroad. This is different from purchases of goods, which can be bought VAT-free on the basis that you pay import duty and VAT on bringing it into your own country. However VAT is immensely complicated so I may be wrong.