Through my experience setting up bank accounts with Brick and Mortar banks and EMI's as well. I can say that Lithuania has some valid options for both EMI's and Banks, some offer dedicated EU IBAN's for any form of account. The transaction fees are minimal and the onboarding process takes up to 2 weeks at the most.
If that's not your cup of tea, have a look at some of the EMI's in Germany, the UK, and Dominica. Most of the EMI's there provide a dedicated IBAN.